Catalogue of Physics Experiments® by LEYBOLD DIDACTIC GMBH, 2001 Printed in the Federal Republic of Germany We reserved the right to make changes in construction and design, and to correct errors; similarly all rights as regards to translation, publication of extracts and photomechanical or electronic reproduction are reserved. All trademarks acknowledged. LEYBOLD DIDACTIC GMBH · Leyboldstrasse 1 · 50354 Huerth · Phone +49 (0)22 33-6 04-0 · Telefax +49 (0)22 33-6 04-222 · email:
[email protected] Printed in the Federal Republic of Germany Mechanics Heat Electricity Electronics Optics Atomic and nuclear physics Solid-state physics Register n n n n n n n n P1 Mechanics P 1.1 Measuring methods P 1.2 Forces P 1.3 Translational motions of a mass point Path, velocity, acceleration, Newton's laws, conservation of linear momentum, free fall, inclined projection, one-dimensional and twodimensional motions P 1.4 Rotational motions of a rigid body Angular velocity, angular acceleration, conservation of angular momentum, centrifugal force, motions of a gyroscope, moment of inertia Measuring length, volume and density, determining the gravitational constant Force as vector, lever, block and tackle, inclined plane, friction P2 Heat P 2.1 Thermal expansion Thermal expansion of solid bodies and liquids, anomaly of water P 2.2 Heat transfer P 2.3 Heat as a form of energy Mixing temperatures, heat capacities, conversion of mechanical and electrical energy into heat energy P 2.4 Phase transitions Thermal conduction, solar collector Melting heat and evaporation heat, vapor pressure, critical temperature P3 Electricity P 3.1 Electrostatics P 3.2 Principles of electricity Charge transport, Ohm's law, Kirchhoff's laws, internal resistance of measuring instruments, electrolysis, electrochemistry P 3.3 Magnetostatics P 3.4 Electromagnetic induction Voltage impulse, induction, eddy currents, transformer, measuring the Earth's magnetic field Electrometer, Coulomb's law, lines of electric flux and isoelectric lines, force effects, charge distributions, capacitance, plate capacitor Permanent magnetism, electromagnetism, magnetic dipole moment, effects of force, BiotSavart's law P4 Electronics P 4.1 Components and basic circuits Current and voltage sources, special resistors, diodes, transistors, optoelectronics P 4.2 Operational amplifier Internal design of an operational amplifier, operational amplifier circuits P 4.3 Open- and closed-loop control Open-loop control technology, closed-loop control technology P 4.4 Digital technology Basic logical operations, switching networks and units, arithmetic units, digital control systems, central processing unit, microprocessor P5 Optics P 5.1 Geometrical optics P 5.2 Dispersion and chromatics Refractive index and dispersion, decomposition of white light, color mixing, absorption spectra P 5.3 Wave optics P 5.4 Polarization Reflection, diffraction, laws of imaging, image distortion, optical instruments Diffraction, two-beam interference, Newton's rings, interferometer, holography Linear and circular polarization, birefringence, optical activity, Kerr effect, Pockels effect, Faraday effect P6 Atomic and nuclear physics P 6.1 Introductory experiments Oil-spot experiment, Millikan experiment, specific electron charge, Planck's constant, dualism of wave and particle, Paul trap P 6.2 Atomic shell P 6.3 X-rays P 6.4 Radioactivity Balmer series, line spectra, inelastic electron collisions, Franck-Hertz experiment, critical potential, ESR, Zeeman effect, optical pumping Detection, attenuation, fine structure, Bragg reflection, Duane and Hunt's law, Moseley's law, Compton effect Detection, Poisson distribution, radioactive decay and half-life, attenuation of R, T, H radiation P7 Solid-state physics P 7.1 Properties of crystals Structure of crystals, x-ray structural analysis, elastic and plastic deformation P 7.2 Conduction phenomena Hall effect, electrical conduction, photoconductivity, luminescence, thermoelectricity, superconductivity P 7.3 Magnetism P 7.4 Scanning probe microscopy Scanning tunneling microscope Dia-, para- and ferromagnetism, ferromagnetic hysteresis P 1.5 Oscillations P 1.6 Wave mechanics P 1.7 Acoustics P 1.8 Aerodynamics and hydrodynamics Barometry, hydrostatic pressure, buoyancy, viscosity, surface tension, aerodynamics, air resistance, wind tunnel Mathematical and physical pendulum, harmonic oscillations, torsional oscillations, coupling of oscillations Transversal and longitudinal waves, wave machine, thread waves, water waves Oscillations of a string, wavelength and velocity of sound, sound, ultrasound, doppler effect, Fourier analysis P 2.5 Kinetic theory of gases Brownian motion of molecules, laws of gases, specific heat of gases P 2.6 Thermodynamic cycle Hot-air engine, heat pump P 3.5 Electrical machines Electric generators, electric motors, three-phase machines P 3.6 DC and AC circuits P 3.7 Electromagnetic oscillations and waves Oscillator circuit, decimeter waves, microwaves, dipole radiation P 3.8 Moving charge carriers in a vacuum Tube diode, tube triode, Maltese-cross tube, Perrin tube, Thomson tube P 3.9 Electrical conduction in gases Self-maintained and nonself-maintained discharge, gas discharge at reduced pressure, cathode and canal rays Capacitor and coil, impedances, measuring bridges, AC voltages and currents, electrical work and power, electromechanical devices P 5.5 Light intensity P 5.6 Velocity of light Measurement according to Foucault/Michelson, measuring with short light pulses, measuring with an electronically modulated signal P 5.7 Spectrometer Quantities and measuring methods of lighting engineering, Stefan-Boltzmann law, Kirchhoff’s laws of radiation Prism spectrometer, grating spectrometer P 6.5 Nuclear physics Particle tracks, Rutherford scattering, NMR, R spectroscopy, H spectroscopy, Compton effect How to use the catalogue 1) Branch 2) Subbranch Light Intensity P 5.5.1 Quantities and measuring methods of lighting engineering P 5.5.1.1 Determining the radiant flux density and the luminous intensity of a halogen lamp P 5.5.1.2 Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY P 5.5.1.3 Verifying Lambert’s law of radiation Optics 3) Topic Group 4) Experiment Topics (each experiment is identified by “P“ plus a 4-digit-number) Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY (P 5.5.1.2) Short experiment descriptions There are two types of physical quantities used to characterize the brightness of light sources: quantities which refer to the physics of radiation, which describe the energy radiation in terms of measurements, and quantities related to lighting engineering, which describe the subjectively perceived brightness under consideration of the spectral sensitivity of the human eye. The first group includes the irradiance Ee, which is the radiated power per unit of area Fe. The corresponding unit of measure is watts per square meter. The comparable quantity in lighting engineering is illuminance E, i. e. the emitted luminous flux per unit of area F, and it is measured in lumens per square meter, or lux for short. In the first experiment, the irradiance is measured using the Moll’s thermopile, and the luminous flux is measured using a luxmeter. The luxmeter is matched to the spectral sensitivity of the human eye V (Ö) by means of a filter placed in front of the photoelement. A halogen lamp serves as the light source. From its spectrum, most of the visible light is screened out using a color filter; subsequently, a heat filter is used to absorb the infrared component of the radiation. The second experiment demonstrates that the luminous intensity is proportional to the square of the distance between a point-type light source and the illuminated surface. The aim of the third experiment is to investigate the angular distribution of the reflected radiation from a diffusely reflecting surface, e.g. matte white paper. To the observer, the surface appears uniformly bright; however, the apparent surface area varies with the cos of the viewing angle. The dependency of the luminous intensity is described by Lambert’s law of radiation: Ee (F) = Ee (0) · cos F P 5.5.1.2 (a) P 5.5.1.2 (b) 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 Cat. No. Description 450 64 450 63 450 68 521 25 450 66 450 60 450 51 562 73 468 03 460 26 460 03 460 22 557 36 532 13 524 010 666 243 524 051 524 200 666 230 460 43 460 40 59013 590 02 301 01 300 02 300 01 501 46 501 33 Halogen lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Halogen lamp, 12 V/50 W Transformer 2 ... 12 V Picture slider for halogen lamp housing Lamp housing Lamp, 6 V/30 W Transformer, 6 V AC, 12 V AC/30 VA Monochromatic light filter, red Iris diaphragm Lens f = + 100 mm Holder with spring clips Moll’s thermopile Microvoltmeter Sensor CASSY Lux sensor Lux box CASSY Lab Hand-held Lux-UV-IR-Meter Small optical bench Swivel joint with angle scale Insulated stand rod, 25 cm long Small clip plug Leybold multiclamp Stand base, V-shape, 20 cm Stand base, V-shape, 28 cm Pair of cables, 100 cm, red and blue Connecting leads, dia. 2.5 mm2, 100 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 2 1 Equipment Lists 1st column P 5.5.1.1 2nd and 3rd column P 5.5.1.2 (a) / (b) same experiment with a different setup 4th column P 5.5.1.3 2 1 194 We would appreciate to prepare and provide additional equipment lists on your request. 6 P 5.5.1.3 1 1 1 1 1 1 1 1 1 2 2 1 4 2 1 2 P 5.5.1.1 Mechanics Table of contents Mechanics P1 Mechanics P 1.1 P 1.1.1 P 1.1.2 P 1.1.3 Measuring methods Measuring length Measuring volume and density Determining the gravitational constant 9 10 11–12 P 1.6 P 1.6.1 P 1.6.2 P 1.6.3 P 1.6.4 P 1.6.5 Wave mechanics Transversal and longitudinal waves Wave machine Circularly polarized waves Propagation of water waves Interference with water waves 46 47 48 49 50 P 1.2 P 1.2.1 P 1.2.2 P 1.2.3 P 1.2.4 P 1.2.5 P 1.2.6 Forces Static effects of forces Force as vector Lever Block and tackle Inclined plane Friction 13 14 15 16 17 18 P1.7 P 1.7.1 P 1.7.2 P 1.7.3 P 1.7.4 P 1.7.5 P 1.7.6 P 1.7.7 Acoustics Sound waves Oscillations of a string Wavelength and velocity of sound Reflection of ultrasonic waves Interference of ultrasonic waves Acoustic Doppler effect Fourier analysis 51 52 53–55 56 57 58 59 P 1.3 P 1.3.1 P 1.3.2 P 1.3.3 P 1.3.4 P 1.3.5 P 1.3.6 P 1.3.7 Translational motions of a mass point One-dimensional motions on the track for students' experiments One-dimensional motions on Fletcher's trolley One-dimensional motions on the linear air track Conservation of linear momentum Free fall Angled projection Two-dimensional motions on the air table 19 20–22 23–25 26–27 28–29 30 31–32 P 1.8 P 1.8.1 P 1.8.2 P 1.8.3 P 1.8.4 P 1.8.5 P 1.8.6 P 1.8.7 Aerodynamics and hydrodynamics Barometry Bouyancy Viscosity Surface tension Introductory experiments in aerodynamics Measuring air resistance Measurements in a wind tunnel 60 61 62 63 64 65 66 P 1.4 P 1.4.1 P 1.4.2 P 1.4.3 P 1.4.4 P 1.4.5 Rotational motions of a rigid body Rotational motions Conservation of angular momentum Centrifugal force Motions of a gyroscope Moment of inertia 33–34 35 36–37 38 39 P 1.5 P 1.5.1 P 1.5.2 P 1.5.3 P 1.5.4 Oscillations Mathematical and physical pendulum Harmonic oscillations Torsion pendulum Coupling of oscillations 40 41 42–43 44–45 8 Mechanics Measuring methods P 1.1.1 Measuring length P 1.1.1.2 P 1.1.1.1 P 1.1.1.2 P 1.1.1.3 Using a caliper gauge with vernier Using a micrometer screw Using a spherometer to determine bending radii P 1.1.1.3 P 1.1.1.1 Caliper gauge, micrometer screw, spherometer Cat. No. 311 54 311 83 311 86 550 35 550 39 460 291 662 092 664 154 664 157 Description Precision vernier callipers Precision micrometer Spherometer Copper wire, 100 m, 0.20 mm dia. Brass wire, 50 m, 0.50 mm dia. Glass mirror, 115 x 100 mm Cover slips, 22 x 22 mm, set of 100 Watch glass dish, 80 mm dia. Watch glass dish, 125 mm dia. 1 1 1 1 1 1 1 1 1 The caliper gauge, micrometer screw and spherometer are precision measuring instruments; their use is practiced in practical measuring exercises. In the first experiment, the caliper gauge is used to determine the outer and inner dimensions of a test body. The vernier scale of the caliper gauge increases the reading accuracy to 1/20 mm. Different wire gauges are measured in the second experiment. In this exercise a fundamental difficulty of measuring becomes apparent, namely that the measuring process changes the measurement object. Particularly with soft wire, the measured results are too low because the wire is deformed by the measurement. The third experiment determines the bending radii R of watchglasses using a spherometer. These are derived on the basis of the convexity height h at a given distance r between the feet of the spherometer, using the formula 2 R=r +h 2h 2 P 1.1.1.2 P 1.1.1.3 P 1.1.1.1 Vertical section through the measuring configuration with spherometer Left: object with convex surface. Right: Object with concaves surface. 9 Measuring methods P 1.1.2 Determining volume and density P 1.1.2.1 Determining the volume and density of solids P 1.1.2.2 Determining the density of liquids using the Mohr density balance P 1.1.2.3 Determining the density of liquids using the pyknometer after Gay-Lussac P 1.1.2.4 Determining the density of air Mechanics Determining the density of air (P 1.1.2.4) Depending on the respective aggregate state of a homogeneous substance, various methods are used to determine its density r=m V m: mass, V: volume The mass and volume of the substance are usually measured separately. To determine the density of solid bodies, a weighing is combined with a volume measurement. The volumes of the bodies are determined from the volumes of liquid which they displace from an overflow vessel. In the first experiment, this principle is tested using regular bodies for which the volumes can be easily calculated from their linear dimensions. To determine the density of liquids, the Mohr density balance is used in the second experiment, and the pyknometer after GayLussac is used in the third experiment. In both cases, the measuring task is to determine the densities of water-ethanol mixtures. The Mohr density balance determines the density from the buoyancy of a body of known volume in the test liquid. The pyknometer is a pear-shaped bottle in which the liquid to be investigated is filled for weighing. The volume capacity of the pyknometer is determined by weighing with a liquid of known density (e.g. water). In the final experiment, the density of air is determined using a sphere of known volume with two stop-cocks. The weight of the enclosed air is determined by finding the difference between the overall weight of the air-filled sphere and the empty weight of the evacuated sphere. P 1.1.2.2 P 1.1.2.3 2 1 1 1 1 Cat. No. 361 44 665 754 665 755 590 06 300 76 311 54 315 05 316 07 361 63 590 33 666 145 382 21 379 07 667 072 375 58 309 42 671 9720 309 48 Description Glass cylinder with 3 tubes Graduated cylinder, 100 ml : 1 Graduated cylinder, 250 ml : 2 Plastic beaker, 1000 ml Laboratory stand II Precision vernier callipers School and laboratory balance 311, 311 g Density balance (Mohr Westphal) Set of 2 cubes and 1 ball Set of 2 gauge blocks Pycnometer, 50 ml Stirring thermometer, -30 to +110 °C Sphere with two cocks Supporting ring for round-bottom flask, 250 ml Hand vacuum and pressure pump Colouring, red, water soluble Ethanol, fully denaturated, 1 l Cord, 10 m 1 2 1 1 1 1 1 1 1 1 1 1 1 1 Determining the density of liquids using the Mohr density balance (P 1.1.2.2) 10 P 1.1.2.4 1 1 1 P 1.1.2.1 Mechanics Measuring methods P 1.1.3 Determining the gravitational constant P 1.1.3.1 Determining the gravitational constant with the gravitation torsion balance after Cavendish – measuring the excursion with a light pointer Determining the gravitational constant with the gravitation torsion balance after Cavendish – measuring the excursion with a light pointer (P 1.1.3.1) Cat. No. 332 101 471 830 Description Gravitation torsion balance He-Ne laser 0.2/1 mW max., linearly polarized Stopclock Steel tape measure, 2m Stand base, V-shape, 20 cm Rotatable clamp Leybold multiclamp Stand rod, 47 cm 1 1 1 1 1 1 1 1 313 05 311 77 300 02 301 03 301 01 300 42 The heart of the gravitation torsion balance after Cavendish is a light-weight beam horizontally suspended from a thin torsion band and having a lead ball with the mass m2 = 15 g at each end. These balls are attracted by the two large lead spheres with the mass m1 = 1.5 kg. Although the attractive force m · m2 F=G· 1 r2 r: distance between sphere midpoints is less than 10-9 N, it can be detected using the extremely sensitive torsion balance. The motion of the small lead balls is observed and measured using a light pointer. Using the curve over time of the motion, the mass m1 and the geometry of the arrangement, it is possible to determine the gravitational constant G using either the end-deflection method or the acceleration method. In the end-deflection method, a measurement error of less than 5 % can be achieved through careful experimenting. The gravitational force is calculated from the resting position of the elastically suspended small lead balls in the gravitational field of the large spheres and the righting moment of the torsion band. The righting moment is determined dynamically using the oscillation period of the torsion pendulum. The acceleration method requires only about 1 min. observation time. The acceleration of the small balls by the gravitational force of the large spheres is measured, and the position of the balls as a function of time is registered. In this experiment, the light pointer is a laser beam which is reflected in the concave reflector of the torsion balance onto a scale. Its position on the scale is measured manually point by point as a function of time. Diagram of light-pointer configuration P 1.1.3.1 11 Measuring methods P 1.1.3 Determining the gravitational constant P 1.1.3.2 Determining the gravitational constant with the gravitation torsion balance after Cavendish – recording the deflections and evaluating the measurement with the IR position detector and PC Determining the gravitational constant with the gravitation torsion balance after Cavendish – recording the deflections and evaluating the measurement with the IR position detector and recorder Mechanics P 1.1.3.3 Determining the gravitational constant with the gravitation torsion balance after Cavendish – recording the deflections and evaluating the measurement with the IR position detector and PC (P 1.1.3.2) The IR position detector (IRPD) enables automatic measurement of the motion of the lead balls in the gravitation torsion balance. The four IR diodes of the IRPD emit an infrared beam; the concave mirror on the torsion pendulum of the balance reflects this beam onto a row of 32 adjacent phototransistors. A microcontroller switches the four IR diodes on in sequence and then determines which phototransistor is illuminated each time. The primary S range of illumination is determined from the individual measurements. The IRPD is supplied complete with a disk containing Windows software for direct measurement and evaluation. The data are registered via the serial interface RS 232 using a computer, or alternatively with a Yt-recorder. The system offers a choice of either the end-deflection or the acceleration method for measuring and evaluating. P 1.1.3.2 1 1 1 1 1 1 1 1 Cat. No. 332 101 332 11 Description Gravitation torsion balance IR position detector 1 1 575 70 3 460 32 460 351 460 352 300 41 530 008 501 46 Yt-recorder, single channel Precision optical bench, standardized cross section, 1 m Optics rider, H = 60 mm/W = 50 mm Optics rider, H = 90 mm/W = 50 mm Stand rod, 25 cm FUNCABLE Pair of cables, 1 m, red and blue additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 Diagram of IR position detector 12 P 1.1.3.3 Mechanics Statics P 1.2.1 Static effects of forces P 1.2.1.1 Confirming Hooke’s law using the helical spring P 1.2.1.2 Bending of a leaf spring Confirming Hooke’s law using a helical spring (P 1.2.1.1) – Bending of a leaf spring (P 1.2.1.2) Cat. No. 352 07 352 08 352 051 340 85 301 21 301 27 301 26 301 25 666 615 311 78 301 29 340 811 Description Helical spring, 5 N, 0.1 N/cm Helical spring, 5 N, 0.25 N/cm Leaf spring I = 435 mm Set of 6 weights, 50 g each Stand base MF Stand rod, 50 cm, 10 mm dia. Stand rod, 25 cm, 10 mm dia. Clamping block MF Universal bosshead, 28 mm dia., 50 mm Tape measure, 1.5 m / 1 mm Pair of pointers Plug-in axle Metal plate Cord, 10 m 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 Forces can be recognized by their effects. Thus, static forces can e.g. deform a body. It becomes apparent that the deformation is proportional to the force acting on the body when this force is not too great. The first experiment shows that the extension s of a helical spring is directly proportional to the force Fs. Hooke’s law applies: Fs = –D · s D: spring constant The second experiment examines the bending of a leaf spring arrested at one end in response to a known force generated by hanging weights from the free end. Here too, the deflection is proportional to the force acting on the leaf spring. 20065559 309 48 P 1.2.1.2 P 1.2.1.1 Schematic diagram of bending of a leaf spring 13 Statics P 1.2.2 Force as a vector Mechanics P 1.2.2.1 Composition and resolution of forces Composition and resolution of forces (P 1.2.2.1 a) The nature of force as a vectorial quantity can be easily and clearly verified in experiments on the adhesive magnetic board. The point of application of all forces is positioned at the midpoint of the angular scale on the adhesive magnetic board, and all individual forces and the angles between them are measured. The underlying parallelogram of forces can be graphically displayed on the adhesive magnetic board to facilitate understanding. In this experiment, a force F is compensated by the spring force of two dynamometers arranged at angles a1 and a2 with respect to F. The component forces F1 and F2 are determined as a function of a1 and a2. This experiment verifies the relationships F = F1 · cos a1 + F2 · cos a2 and 0 = F1 · sin a1 + F2 · sin a2 . Cat. No. 301301 301300 314215 301331 35208 31177 34261 30101 30044 30107 20065559 Description Adhesive magnetic board Demonstration-experiment frame Round dynamometer 5 N Magnetic base with hook Helical spring, 5 N, 0.25 N/cm Steel tape measure, 2 m Set of 12 weights, 50 g each Leybold multiclamp Stand rod, 100 cm Simple bench clamp Metal plate P 1.2.2.1 (a) 1 2 1 1 1 1 4 2 2 4 Parallelogram of forces Setup with demonstration-experiment frame (P 1.2.2.1 b) 14 P 1.2.2.1 (b) 1 1 2 1 1 1 1 Mechanics P 1.2.3 Levers Statics P 1.2.3.1 One-sided and two-sided lever P 1.2.3.2 Wheel and axle as a lever with unequal sides Two-sided lever (P 1.2.3.1) Cat. No. 342 60 342 75 342 61 314 45 314 46 300 02 301 01 300 42 Description Lever on ball bearing, 1 m long Metal wheel and axle Set of 12 weights, 50 g each Spring balance, 2.0 N Spring balance, 5.0 N Stand base, V-shape, 20 cm Leybold multiclamp Stand rod, 47 cm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 In physics, the law of levers forms the basis for all forms of mechanical transmission of force. This law can be explained using the higher-level concept of equilibrium of angular momentum. The first experiment examines the law of levers: F1 · x1 = F2 · x2 for one-sided and two-sided levers. The object is to determine the force F1 which maintains a lever in equilibrium as a function of the load F2, the load arm x2 and the power arm x1. The second experiment explores the equilibrium of angular momentum using a wheel and axle. This experiment broadens the understanding of the concepts force, power arm and line of action, and explicitly proves that the absolute value of the angular momentum depends only on the force and the distance between the axis of rotation and the line of action. P 1.2.3.2 P 1.2.3.1 Equilibrium of angular momentum on a wheel and axle (P 1.2.3.2) 15 Statics P 1.2.4 Block and tackle Mechanics P 1.2.4.1 Fixed pulley, loose pulley and block and tackle as simple machines P 1.2.4.2 Fixed pulley, loose pulley and block and tackle as simple machines on the adhesive magnetic board Fixed pulley, loose pulley and block and tackle as simple machines on the adhesive magnetic board (P 1.2.4.2 b) The fixed pulley, loose pulley and block and tackle are classic examples of simple machines. Experiments with these machines represent the most accessible introduction to the concept of work in mechanics. The experiments are offered in two equipment variations. In the first variation, the block and tackle is set up on the lab bench using a stand base. The block and tackle can be expanded to three pairs of pulleys and can support loads of up to 20 N. The pulleys are mounted virtually friction-free in ball bearings. The setup on the adhesive magnetic board in the second variation has the advantage that the amount and direction of the effective forces can be represented graphically directly at the source. Also, this arrangement makes it easy to demonstrate the relationship to other experiments on the statics of forces, providing these can also be assembled on the adhesive magnetic board. Cat. No. 342 28 301 301 301 300 341 65 340 911 340 921 340 930 340 87 301 330 301 331 301 332 314 212 314 215 314 181 315 36 342 61 300 01 300 44 301 01 301 07 309 50 Description Pulley block, 20 N Adhesive magnetic board Demonstration-experiment-frame Pulley with hook and rod Pulley, plug-in, 50 mm diameter Pulley, plug-in, 100 mm diameter Pulley bridge Load hook Magnetic base with 4-mm socket Magnetic base with noon Magnetic base with 4-mm axis Round dynamometer 2 N Round dynamometer 5 N Precision dynamometer, 20.0 N Set 7 weights, 0.1 - 2 kg, with hook Set of 12 weights, 50 g each Stand base, V-shape, 28 cm Stand rod, 100 cm Leybold multiclamp Simple bench clamp Demonstration cord, 20m (polyamide) 1 1 1 1 2* 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 4 2 1 4 1 1 2 2 2 2 1 1 1 1 1 20065 559 Metal plate * additionally recommended Setup with block and tackle (P 1.2.4.1) 16 P 1.2.4.2 (b) P 1.2.4.2 (a) P 1.2.4.1 Mechanics P 1.2.5 Inclined plane Statics P 1.2.5.1 Inclined plane: force along the plane and force normal to the plane P 1.2.5.2 Determining the coefficient of static friction using the inclined plane Inclined plane: force along the plane and force normal to the plane (P 1.2.5.1) Cat. No. 341 21 314 141 342 10 311 77 Description Inclined plane with trolley and screw model Precision dynamometer, 1.0 N Pair of wooden blocks for friction experiments Steel tape measure, 2m 1 1 1 1 1 The motion of a body on an inclined plane can be described most easily when the force exerted by the weight G on the body is vectorially decomposed into a force F1 along the plane and a force F2 normal to the plane. The force along the plane acts parallel to a plane inclined at an angle a, and the force normal to the plane acts perpendicular to the plane. For the absolute values of the forces, we can say: F1 = G · sin a and F2 = G · cos a This decomposition is verified in the first experiment. Here, the two forces F1 and F2 are measured for various angles of inclination a using precision dynamometers. The second experiment uses the dependency of the force normal to the plane on the angle of inclination for quantitative determination of the coefficient of static friction m of a body. The inclination of a plane is increased until the body no longer adheres to the surface and begins to slide. From the equilibrium of the force along the plane and the coefficient of static friction F1 = m · F2 we can derive m = tan a. P 1.2.5.2 P 1.2.5.1 Calculating the coefficient of static friction m (P 1.2.5.2) 17 Statics P 1.2.6 Friction Mechanics P1.2.6.1 Static friction, sliding friction and rolling friction Static friction, sliding friction and rolling friction (P 1.2.6.1) In discussing friction between solid bodies, we distinguish between static friction, sliding friction and rolling friction. Static friction force is the minimum force required to set a body at rest on a solid base in motion. Analogously, sliding friction force is the force required to maintain a uniform motion of the body. Rolling friction force is the force which maintains the uniform motion of a body which rolls on another body. To begin, this experiment verifies that the static friction force FH and the sliding friction force FG are independent of the size of the contact surface and proportional to the resting force G on the base surface of the friction block. Thus, the following applies: FH = mH · G and FG = mG · G. The coefficients mH and mG depend on the material of the friction surfaces. The following relationship always applies: mH > mG. To distinguish between sliding and rolling friction, the friction block is placed on top of multiple stand rods laid parallel to each other. The rolling friction force FR is measured as the force which maintains the friction block in a uniform motion on the rolling rods. The sliding friction force FG is measured once more for comparison, whereby this time the friction block is pulled over the stand rods as a fixed base (direction of pull = direction of rod axes). This experiment confirms the relationship: F G > F R. Cat. No. 315 36 300 40 314 47 342 10 Description Set 7 weights, 0.1 – 2 kg, with hook Stand rod, 10 cm Spring balance, 10.0 N Pair of wooden blocks for friction experiments 18 P 1.2.6.1 1 6 1 1 Mechanics Translational motions of a mass point P 1.3.1 One-dimensional motions on the track for students’ experiments P1.3.1.1 Recording path-time diagrams of linear motions Recording path-time diagrams of linear motions (P 1.3.1.1) Cat. No. 588 813S 521 210 Description STM equipment set Mechanics 3 (MEC 3) Transformer, 6 V AC, 12 V AC/ 30 W Cord, 10 m 1 1 1 tape strips, or the instantaneous velocity, increase for equal time intervals. The increase in length, and thus the instantaneous acceleration 1 ai = (vi+1 – vi), Dt is constant within the attainable measuring accuracy. From the velocity-time diagram, we can recognize the linear function v=a·t a: average acceleration and from the path-time diagram the function 1 s= a · t2. 2 309 48 The motion of Fletcher’s trolley on a track is recorded using a strip of paper which the trolley pulls through a recorder. The device marks the respective position on the measurement tape at fixed intervals (e. g. Wt = 0.1 s). The experiment first investigates uniform motions of the trolley. The marked positions on the register tape are measured and entered in a path-time diagram as value pairs (si, ti). From the diagram, it is possible to recognize the linear function s=v·t v: average velocity In the further evaluation, the paper register tape is cut at the position marks and the sections are placed side by side in a row. Their lengths correspond to the instantaneous velocities 1 · (si+1 – si), vi = Dt which agree with the average velocity v within the context of the measuring accuracy. Uniformly accelerated motion of the trolley on the inclined track is subsequently evaluated in the same way. Additionally, the instantaneous velocities vi are plotted in a velocity-time diagram as value pairs (vi, ti). Unlike uniform motions, the lengths of the P 1.3.1.1 Velocity-time diagram of a uniformly accelerated motion 19 Translational motions of a mass point P 1.3.2 One-dimensional motions with Fletcher’s trolley P 1.3.2.1 Recording the path-time diagrams of linear motions – measuring the time with the electronic stopclock Mechanics Recording the path-time diagrams of linear motions – measuring the time with the electronic stopclock (P 1.3.2.1b) Fletcher’s trolley is the classical experiment apparatus for investigating linear translational motions. The trolley has a ball bearing, his axles are spring-mounted and completely immerged in order to prevent being overloaded. The wheels are designed in such a way that the trolley centers itself on the track and friction at the wheel flanks is avoided. Using extremely simple means, this experiment makes the definition of the velocity v as the quotient of the path difference Ds and the corresponding time difference Dt directly accessible to the students. The path difference Ds is read off directly from a scale on the track. Depending on the chosen equipment configuration a or b, electronic measurement of the time difference is started and stopped using either a key and a light barrier or two light barriers. To enable investigation of uniformly accelerated motions, the trolley is connected to a thread which is laid over a pulley, allowing various weights to be suspended. Cat. No. Description 337 130 337 110 337 114 315 410 315 418 337 462 337 463 337 464 683 41 313 033 501 16 309 48 501 46 Track, 1.5 m Trolley Additional weights Slotted weight hanger, 10 g Slotted weight, 10 g Combination light barrier Holder for combination spoked wheel Combination spoked wheel Holding magnet Electronic stopclock P Multicore cable, 6-pole, 1.5 m long Cord, 10 m Pair of cables, 1 m, red and blue * additionally recommended P 1.3.2.1(a) 1 1 1* 1 4 2 1 1 1 2 1 Path-time diagram of a linear motion 20 P 1.3.2.1(b) 1 1 1* 1 4 1 1 1 1 1 1 1 1 Mechanics Translational motions of a mass point P1.3.2 One-dimensional motions with Fletcher’s trolley P 1.3.2.2 Recording the path-time diagrams of linear motions – recording and evaluating with CASSY P 1.3.2.3 Definition of the Newton as a unit of force – recording and evaluating with CASSY Recording the path-time diagrams of linear motions – recording and evaluating with CASSY (P 1.3.2.2) Cat. No. 337 130 337 110 315 410 315 418 337 114 337 115 337 462 337 464 683 41 524 010 524 034 524 200 501 16 309 48 501 46 Description Track, 1.5 m Trolley Slotted weight hanger, 10 g Slotted weight, 10 g Additional weights Newton weights Combination light barrier Combination spoked wheel Holding magnet Sensor-CASSY Timer box CASSY Lab Multicore cable, 6-pole, 1.5 m long Cord, 10 m Pair of cables, 1 m, red and blue additionally required: 1 PC with windows 95/NT or higher 1 1 1 4 1* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The first experiment looks at motion events which can be transmitted to the combination spoked wheel by means of a thin thread on Fletcher’s trolley. The combination spoked wheel serves as an easy-running deflection pulley, and at the same time enables path measurement using the combination light barrier. The signals of the combination light barrier are recorded by the computer-assisted measuring system CASSY and converted to a path-time diagram. As this diagram is generated in real time while the experiment is running, the relationship between the motion and the diagram is extremely clear. In the second experiment, a calibrated weight exercises an accelerating force of 1 N on a trolley with the mass 1 kg. As one might expect, CASSY shows the value m a=1 2 s for the acceleration. At the same time, this experiment verifies that the trolley is accelerated to the velocity m v=1 s in the time 1 s. P 1.3.2.2 P 1.3.2.3 21 Translational motions of a mass point P 1.3.2 One-dimensional motions with the Fletcher's trolley P 1.3.2.4 Recording the path-time diagrams of linear motions – recording and evaluating with VideoCom Mechanics Recording the path-time diagrams of linear motions – recording and evaluating with VideoCom (P 1.3.2.4) The single-line CCD video camera VideoCom represents a new, easy-to-use method for recording one-dimensional motions. It illuminates one or more bodies in motion with LED flashes and images them on the CCD line with 2048-pixel resolution via a camera lens (CCD: charge-coupled device). A piece of retroreflecting foil is attached to each of the bodies to reflect the light rays back to the lens. The current positions of the bodies are transmitted to the computer up to 80 times per second via the serial interface. The automatically controlled flash operates at speeds of up to 1/800 s, so that even a rapid motion on the linear air track or any other track can be sharply imaged. The software supplied with VideoCom represents the entire motion of the bodies in the form of a path-time diagram, and also enables further evaluation of the measurement data. Cat. No. Description 337 130 337 110 315 410 315 418 337 114 337 463 337 464 683 41 337 47 Track, 1.5 m Trolley Slotted weight hanger, 10 g Slotted weight, 10 g Additional weights Holder for combination spoked wheel Combination spoked wheel Holding magnet VideoCom 300 59 309 48 501 38 Camera tripod Cord, 10 m Connecting lead, Ø 2.5 mm2, 200 cm additionally required: PC with Windows 95/NT or higher * additionally recommended 22 P 1.3.2.4 1 1 1 4 1* 1 1 1 1 1 1 4 1 Mechanics Translational motions of a mass point P 1.3.3 One-dimensional motions on the linear air track P 1.3.3.1 Recording the path-time diagrams of linear motions – measuring the time with the Morse key and forked light barrier Recording the path-time diagrams of linear motions – measuring the time with the Morse key and forked light barrier (P 1.3.3.1) Cat. No. Description 337 501 337 53 667 823 311 02 337 46 524 010 524 034 524 200 501 16 575 48 300 40 501 46 Linear air track, 1.5 m long, complete Air supply for air track Power controller Metal scale, 1 m long Forked light barrier, infra-red Sensor-CASSY Timer box CASSY Lab Multicore cable, 6-pole, 1.5 m long Digital counter Stand rod, 10 cm Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 The advantage of studying linear translational motions on the linear air track is that interference factors such as frictional forces and moments of inertia of wheels do not occur. The sliders on the linear air track are fitted with an interrupter flag which obscures a light barrier. By adding additional weights, it is possible to double and triple the masses of the sliders. Using extremely simple means, this experiment makes the definition of the velocity v as the quotient of the path difference Ds and the corresponding time difference Dt directly accessible to the students. The path difference Ds is read off directly from a scale on the track. Depending on the chosen equipment configuration, electronic measurement of the time difference is started by switching off the holding magnet or using a light barrier. The instantaneous velocity of the slider can also be calculated from the obscuration time of a forked light barrier and the width of the interrupter flag. To enable investigation of uniformly accelerated motions, the slider is connected to a thread which is laid over a pulley, allowing weights to be suspended. Path-time diagram for uniform motion P 5.2.1.2 P 1.3.3.1 (d) P 5.2.1.1 P 1.3.3.1 (c) P 1.3.3.1 (b) P 1.3.3.1 (a) 23 Translational motions of a mass point P 1.3.3 One-dimensional motions on the linear air track P 1.3.3.4 Recording the path-time diagrams of linear motions – measuring and evaluating with CASSY P 1.3.3.5 Uniformly accelerated motion with reversal of direction – measuring and evaluating with CASSY P 1.3.3.6 Kinetic energy of a uniformly accelerated mass – recording and evaluating with CASSY Mechanics Recording the path-time diagrams of linear motions – measuring and evaluating with CASSY (P 1.3.3.4) The computer-assisted measurement system CASSY is particularly suitable for simultaneously measuring transit time t, path s, velocity v and acceleration a of a slider on the linear air track. The linear motion of the slider is transmitted to the motion sensing element by means of a lightly tensioned thread; the signals of the motion sensing element are matched to the CASSY measuring inputs by the BMW box. In terms of content, the first two experiments are comparable to those conducted using the motion transducer and the Yt recorder. However, the PC greatly simplifies the evaluation of the recorded data. In addition, the data can be exported in the form of a table of discrete values to enable external evaluations. The third experiment records the kinetic energy m 2 E= ·v 2 of a uniformly accelerated slider of the mass m as a function of the time and compares it with the work W=F·s which the accelerating force F has performed. This verifies the relationship E(t) = W(t). Cat. No. Description 337 501 337 53 667 823 Linear air track, 1.5 m long, complete Air supply for air track Power controller 337 631 501 16 524 032 524 010 524 200 501 46 Motion transducer Multicore cable, 6-pole, 1.5 m BMW box Sensor-CASSY CASSY Lab Pair of cables, 100 cm, red and blue additionally required: PC with Windows 95/NT or higher Path-time, velocity-time and acceleration-time diagram 24 P 5.2.1.2 P 1.3.3.4-6 1 1 1 1 1 1 1 1 1 1 P 5.2.1.1 Mechanics Translational motions of a mass point P 1.3.3 One-dimensional motions on the linear air track P 1.3.3.7 Confirming Newton's first and second laws for linear motions – recording and evaluating with VideoCom P 1.3.3.8 Uniformly accelerated motion with reversal of direction – recording and evaluating with VideoCom P 1.3.3.9 Kinetic energy of a uniformly accelerated mass – recording and evaluating with VideoCom Confirming Newton's first and second laws for linear motions – recording and evaluating with VideoCom (P 1.3.3.7) Cat. No. 337 501 300 40 311 02 337 53 667 823 337 47 Description Linear air track, 1.5 m long, complete Stand rod, 10 cm Metal scale, 1 m long Air supply for air track Power controller VideoCom 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 300 59 501 38 Camera tripod Connecting lead, Ø 2.5 mm2, 200 cm, black additionally required: PC with Windows 95/NT or higher 1 4 1 1 4 1 1 4 1 The object of the first experiment is to study uniform and uniformly accelerated motions of a slider on the linear air track and to represent these in a path-time diagram. The software also displays the velocity v and the acceleration a of the body as a function of the transit time t, and the further evaluation verifies Newton's equation of motion F=m·a F: accelerating force, m: mass of accelerated body The other two experiments are identical in terms of content with experiments P 1.3.3.5 and P 1.3.3.6. P 1.3.3.7 P 1.3.3.8 Investigating uniformly accelerated motions with VideoCom P 1.3.3.9 25 Translational motions of a mass point P 1.3.4 Conservation of linear momentum P 1.3.4.1 Energy and linear momentum in elastic collision – measuring with two light barriers and CASSY P 1.3.4.2 Energy and linear momentum in inelastic collision – measuring with two light barriers and CASSY P 1.3.4.3 Rocket principle: conservation of linear momentum and repulsion Mechanics Elastic collision - measuring with two light barriers and CASSY (P 1.3.3.1/2 b) The use of a linear track makes possible superior quantitative results when verifying the conservation of linear momentum in an experiment. Especially on the linear air track it is possible e.g. to minimize the energy “loss” for elastic collision. In the first and second experiments, the obscuration times Dti of two light barriers are measured, e.g. for two bodies on a linear track before and after elastic and inelastic collision. These experiments investigate collisions between a moving body and a body at rest, as well as collisions between two bodies in motion. The evaluation program calculates and, when selected, compares the velocities d vi = , Dti d: width of interrupter flags the momentum values pi = mi · vi mi: masses of bodies and the energies 1 2 Ei = · mi · vi 2 of the bodies before and after collision. In the final experiment, the recoil force on a jet slider is measured for different nozzle cross-sections using a sensitive dynamometer in order to investigate the relationship between repulsion and conservation of linear momentum. Cat. No. Description 337 501 337 53 667 823 337 46 337 56 337 59 314 081 337 130 337 110 337 114 337 112 337 462 524 010 524 200 524 034 501 16 Linear air track, 1.5 m long, complete Air supply for air track Power controller Forked light barrier, infra-red Jet slider with 3 jets Dynamometric device Precision dynamometer, 0.01 N Track, 1.5 m Trolley Additional weights Impact spring for trolley Combination light barrier Sensor-CASSY CASSY Lab Timer box Multicore cable, 6-pole, 1.5 m long additionally required: PC with Windows 95/NT or higher 1 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 26 P 5.2.1.2 P 1.3.4.3 1 1 1 1 1 1 P 1.3.4.2 (b) P 5.2.1.1 P 1.3.4.2 (a) P 1.3.4.1 (b) P 1.3.4.1 (a) Mechanics Translational motions of a mass point P 1.3.4 Conservation of linear momentum P 1.3.4.4 Newton's third law and laws of collision – recording and evaluating with VideoCom Newton's third law and laws of collision – recording and evaluating with VideoCom (P 1.3.4.4 b) Cat. No. Description 337 130 337 110 337 114 337 112 337 501 337 53 667 823 311 02 337 47 Track, 1.5 m Trolley Additional weights Impact spring for trolley Linear air track, 1.5 m long, complete Air supply for air track Power controller Metal scale, 1 m long VideoCom 1 2 1 2 1 1 1 1 1 1 The single-line CCD video camera is capable of recording pictures at a rate of up to 80 pictures per second. This time resolution is high enough to reveal the actual process of a collision (compression and extension of springs) between two sliders on the linear air track. In other words, VideoCom registers the positions s1(t) and s2(t) of the two sliders, their velocities v1(t) and v2(t) as well as their accelerations a1(t) and a2(t) even during the actual collision. The energy and momentum balance can be verified not only before and after the collision, but also during the collision itself. This experiment records the elastic collision of two bodies with the masses m1 and m2. The evaluation shows that the linear momentum p(t) = m1 · v1(t) + m2 · v2(t) remains constant during the entire process, including the actual collision. On the other hand, the kinetic energy E(t) = m1 m · v12(t) + 2 · v22(t) 2 2 300 59 Camera tripod additionally required: PC with Windows 95/NT or higher 1 1 P 1.3.4.4 (b) 1 1 P 1.3.4.4 (a) reaches a minimum during the collision, which can be explained by the elastic strain energy stored in the springs. This experiment also verifies Newton's third law in the form m1 · a1(t) = – m1 · a2(t) From the path-time diagram, it is possible to recognize the time t0 at which the two bodies have the same velocity v1(t0) = v2(t0) and the distance s2 – s1 between the bodies is at its lowest. At time t0, the acceleration values (in terms of their absolute values) are greatest, as the springs have reached their maximum tension. Confirmation of Newton’s third law 27 Translational motions of a mass point P 1.3.5 Free fall Mechanics P 1.3.5.1 Free fall: time measurement with the contact plate and the counter P P 1.3.5.2 Free fall: time measurement with the forked light barrier and digital counter Free fall: time measurement with the contact plate and the counter P (P 1.3.5.1) To investigate free fall, a steel ball is suspended from an electromagnet. It falls downward with a uniform acceleration due to the force of gravity F=m·g m: mass of ball, g: gravitational acceleration as soon as the electromagnet is switched off. The friction of air can be regarded as negligible as long as the falling distance, and thus the terminal velocity, are not too great; in other words, the ball falls freely. In the first experiment, electronic time measurement is started as soon as the ball is released through interruption of the magnet current. After traveling a falling distance h, the ball falls on a contact plate, stopping the measurement of time t. The measurements for various falling heights are plotted as value pairs in a path-time diagram. As the ball is at rest at the beginning of timing, g can be determined using the relationship 1 h = g · t 2. 2 In the second experiment, the ball passes one, or optionally two light barriers on its way down; their distance from the holding magnet h is varied. In addition to the falling time t, the obscuration time Dt is measured and, for a given ball diameter d, the instantaneous velocity d vm = Dt of the ball is determined. A velocity-time diagram vm(t) is prepared in addition to the path-time diagram h(t). Thus, the relationship vm = g · t can be used to determine g. Cat. No. Description 336 23 336 21 Large contact plate Holding magnet with clamp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 200 67 288 Steel ball, 16 mm dia. 521 230 575 451 Low-voltage power supply, 3,6,9,12 V AC/DC,3 A Counter P Morse key Digital counter STE Si diode 1 N 4007 Forked light barrier, infra-red Multicore cable, 6-pole, 1.5 m long Vertical scale, 1 m long 504 52 575 48 578 51 337 46 501 16 311 22 300 01 300 11 300 41 300 44 300 46 301 01 309 48 340 85 501 35 501 25 501 26 501 30 501 31 501 36 Stand base, V-shape, 28 cm Saddle base Stand rod, 25 cm Stand rod, 100 cm Stand rod, 150 cm Leybold multiclamp Cord, 10 m Set of 6 weights, 50 g each Connecting lead, 200 cm, red, Ø 2.5 mm2 Connecting lead, 50 cm, red, Ø 2.5 mm2 Connecting lead, 50 cm, blue, Ø 2.5 mm2 Connecting lead, 100 cm, red, Ø 2.5 mm2 Connecting lead, 100 cm, blue, Ø 2.5 mm2 Connecting lead, 200 cm, blue, Ø 2.5 mm2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 28 P 1.3.5.2 (b) 1 1 1 1 1 1 1 1 1 1 P 1.3.5.2 (a) P 1.3.5.1 Mechanics Translational motions of a mass point P 1.3.5 Free fall P 1.3.5.3 Free fall: multiple time measurements with the g-ladder P 1.3.5.4 Free fall: recording and evaluating with VideoCom Free fall: recording and evaluating with VideoCom (P 1.3.5.4) Cat. No. 337 46 501 16 524 034 529 034 524 010 524 200 337 47 Description Forked light barrier, infra-red Multicore cable, 6-pole, 1.5 m long Timer Box g-ladder Sensor CASSY CASSY Lab VideoCom 1 1 1 1 1 1 1 300 59 337 472 33621 30001 30002 30041 30042 30046 30101 50138 Camera tripod Falling body for VideoCom Holding magnet with clamp Stand base, V-shape, 28 cm Stand base, V-shape, 20 cm Stand rod, 25 cm Stand rod, 47 cm Stand rod, 150 cm Leybold multiclamp Connecting lead, Ø 2.5 mm2, 200 cm, black additionally recommended: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 The disadvantage of preparing a path-time diagram by recording the measured values point by point is that it takes a long time before the dependency of the result on experiment parameters such as the initial velocity or the falling height becomes apparent. Such investigations become much simpler when the entire measurement series of a path-time diagram is recorded in one measuring run using the computer. In the first experiment, a ladder with several rungs falls through a forked light barrier, which is connected to the CASSY computer interface device to measure the obscuration times. This measurement is equivalent to a measurement in which a body falls through multiple equidistant light barriers. The height of the falling body corresponds to the rung width. The measurement data are recorded and evaluated using CASSY LAB. The instantaneous velocities are calculated from the obscuration times and the rung width and displayed in a velocity-time diagram v(t). The measurement points can be described by a straight line v(t) = v0 + g · t g: gravitational acceleration whereby v0 is the initial velocity of the ladder when the first rung passes the light barrier. In the second experiment, the motion of a falling body is tracked as a function of time using the single-line CCD camera VideoCom and evaluated using the corresponding software. The measurement series is displayed directly as the path-time diagram h(t). This curve can be described by the general relationship 1 s = v0 · t + g · t2 2 P 1.3.5.3 Free fall: multiple time measurements with the g-ladder (P1.3.5.3) P 1.3.5.4 1 1 4 1 29 Translational motions of a mass point P 1.3.6 Angled projection Mechanics P 1.3.6.1 Point-by-point recording of the projection parabola as a function of the velocity and angle of projection P 1.3.6.2 Principle of superposing: comparing angled projection and free fall Point-by-point recording of the projection parabola as a function of the velocity and angle of projection (P 1.3.6.1) The trajectory of a ball launched at a projection angle a with a projection velocity v0 can be reconstructed on the basis of the principle of superposing. The overall motion is composed of a motion with constant velocity in the direction of projection and a vertical falling motion. The superposition of these motions results in a parabola, whose height and width depend on the angle and velocity of projection. The first experiment measures the trajectory of the steel ball point by point using a vertical scale. Starting from the point of projection, the vertical scale is moved at predefined intervals; the two pointers of the scale are set so that the projected steel ball passes between them. The trajectory is a close approximation of a parabola. The observed deviations from the parabolic form may be explained through friction with the air. In the second experiment, a second ball is suspended from a holding magnet in such a way that the first ball would strike it if propelled in the direction of projection with a constant velocity. Then, the second ball is released at the same time as the first ball is projected. We can observe that, regardless of the launch velocity v0 of the first ball, the two balls collide; this provides experimental confirmation of the principle of superposing. Cat. No. 336 56 336 21 521 230 Description Large projection apparatus Holding magnet with clamp DC voltage source, approx. U = 10 V, e.g. Low-voltage power supply, 3,6,9,12 V AC/DC, 3 A Wooden ruler, 1 m long Vertical scale, 1 m long Steel tape measure, 2 m Saddle base Stand rod, 100 cm Laboratory stand II Bench clamp Simple bench clamp Connecting lead, Ø 2.5 mm2, 50 cm, blue Connecting lead, Ø 2.5 mm2, 200 cm, red Connecting lead, Ø 2.5 mm2, 200 cm, blue 1 311 03 311 22 311 77 300 11 300 44 300 76 301 06 301 07 501 26 501 35 501 36 1 1 1 1 1 2 2 1 1 1 1 Schematic diagram comparing angled projection and free fall (P 1.3.6.2) 30 P 1.3.6.2 1 1 1 1 P 1.3.6.1 Mechanics Translational motions of a mass point P 1.3.7 Two-dimensional motions on the air table P 1.3.7.1 P 1.3.7.2 P 1.3.7.3 P 1.3.7.4 P 1.3.7.5 Uniform linear motion and uniform circular motion Uniformly accelerated motion Two-dimensional motion on an inclined plane Two-dimensional motion in response to a central force Superimposing translational and rotational motions on a rigid body Uniform linear motion and uniform circular motion (P 1.3.7.1) Cat. No. Description 337 801 352 10 Large air table Helical spring, 2 N; 0.03 N/cm 1 1 1 The air table makes possible recording of any two-dimensional motions of a slider for evaluation following the experiment. To achieve this, the slider is equipped with a recording device which registers the position of the slider on metallized recording paper every 20 ms. The aim of the first experiment is to examine the instantaneous velocity of straight and circular motions. In both cases, their absolute values can be expressed as Ds v= , Dt where Ds is the straight path traveled during time Dt for linear motions and the equivalent arc for circular motions. In the second experiment, the slider without an initial velocity moves on the air table inclined by the angle a. Its motion can be described as a one-dimensional, uniformly accelerated motion. The marked positions permit plotting of a path-time diagram from which we can derive the relationship s s= · a · t2 where a = g · sin a 2 P 5.2.1.2 P 1.3.7.5 1 P 5.2.1.1 P 1.3.7.4 P 1.3.7.1-3 In the third experiment, a motion “diagonally upward” is imparted on the slider on the inclined air table, so that the slider describes a parabola. Its motion is uniformly accelerated in the direction of inclination and virtually uniform perpendicular to this direction. The aim of the fourth experiment is to verify Kepler’s law of areas. Here, the slider moves under the influence of a central force exerted by a centrally mounted helical screw. In the evaluation, the area DA = Ir x DsI “swept” due to the motion of the slider in the time Dt is determined from the radius vector r and the path section Ds as well as from the angle between the two vectors. The final experiment investigates simultaneous rotational and translational motions of one slider and of two sliders joined together in a fixed manner. One recorder is placed at the center of gravity, while a second is at the perimeter of the “rigid body” under investigation. The motion is described as the motion of the center of gravity plus rotation around that center of gravity. 31 Translational motions of a mass point P 1.3.7 Two-dimensional motions on the air table P 1.3.7.6 Two-dimensional motion of two elastically coupled bodies P 1.3.7.7 Experimentally verifying the equality of a force and its opposing force P 1.3.7.8 Elastic collision in two dimensions P 1.3.7.9. Inelastic collision in two dimensions Mechanics Elastic collision in two dimensions (P 1.3.7.8) The air table is supplied complete with two sliders. This means that this apparatus can also be used to investigate e.g. twodimensional collisions. In the first experiment, the motions of two sliders which are elastically coupled by a rubber band are recorded. The evaluation shows that the common center of gravity moves in a straight line and a uniform manner, while the relative motions of the two sliders show a harmonic oscillation. In the second experiment, elastically deformable metal rings are attached to the edges of the sliders before the start of the experiment. When the two rebound, the same force acts on each slider, but in the opposite direction. Therefore, regardless of the masses m1 and m2 of the two sliders, the following relationship applies for the total two-dimensional momentum. m1 · v1 + m2 · v2 = 0 Cat. No. Description 337 801 Large air table The last two experiments investigate elastic and inelastic collisions between two sliders. The evaluation consists of calculating the total two-dimensional momentum p = m1 · v1 + m2 · v2 and the total energy m m E = 1 · v2 + 2 · v2 1 2 2 2 both before and after collision. 32 P 5.2.1.2 P 1.3.7.6-9 1 P 5.2.1.1 Mechanics Rotational motions of a rigid body P 1.4.1 Rotational motions P 1.4.1.1 Path-time diagrams of rotational motions - time measurements with the counter P Path-time diagrams of rotational motions - time measurements with the counter P (P 1.4.1.1 a) Cat. No. Description 347 23 337 46 575 451 Rotation model Forked light barrier, infra-red Counter P 1 1 1 1 2 1 501 16 Multicore cable, 6-pole, 1.5 m 1 1 1 1 2 1 1 1 300 76 301 07 500 411 Laboratory stand II Simple bench clamp Connecting lead, red, 25 cm The low-friction Plexiglas disk of the rotation model is set in uniform or uniformly accelerated motion for quantitative investigations of rotational motions. Forked light barriers are used to determine the angular velocity; their light beams are interrupted by a 10° flag mounted on the rotating disk. When two forked light barriers are used, measurement of time t can be started and stopped for any angle f. This experiment determines the mean velocity f v= . t If only one forked light barrier is available, the obscuration time Dt is measured, which enables calculation of the instantaneous angular velocity 10h. v= Dt In this experiment, the angular velocity v and the angular acceleration a are recorded analogously to acceleration in translational motions. Both uniform and uniformly accelerated rotational motions are investigated. The results are graphed in a velocitytime diagram v(t). In the case of a uniformly accelerated motion of a rotating disk initially at rest, the angular acceleration can be determined from the linear function v = a · t. P 1.4.1.1 (a) P 1.4.1.1 (b) 33 Rotational motions of a rigid body P 1.4.1 Rotational motions Mechanics P 1.4.1.2 Path-time diagrams of rotational motions – measuring and evaluating with CASSY Path-time diagrams of rotational motions – measuring and evaluating with CASSY (P 1.4.1.2) The use of the computer-assisted measured-value recording system CASSY facilitates the study of uniform and uniformly accellerated rotational motions. A thread stretched over the surface of the rotation model transmits the rotational motion to the motion sensing element whose signals are adapted to the measuring inputs of CASSY by the motion transducer box. The topic of this experiment are homogeneous and constantly accellerated rotational motions, which are studied on the analogy of homogeneous and constantly accellerated translational motions. Cat. No. 347 23 337 631 524 010 524 200 524 032 501 16 336 21 300 41 300 11 301 07 300 76 501 46 Description Rotation model Motion sensing element Sensor-CASSY CASSY Lab Motion transducer box Multicore cable, 6-pole, 1.5 m long Holding magnet with clamp Stand rod, 25 cm Saddle base Simple bench clamp Laboratory stand II Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 34 P 1.4.1.2 1 1 1 1 1 1 1 1 1 1 1 1 1 Mechanics Rotational motions of a rigid body P 1.4.2 Conservation of angular momentum P 1.4.2.1 Conservation of angular momentum for elastic torsion impact P 1.4.2.2 Conservation of angular momentum for inelastic torsion impact Conservation of angular momentum for elastic torsion impact (P 1.4.2.1) Cat. No. Description 347 23 300 76 337 46 524 034 501 16 524 010 524 200 Rotation model Laboratory stand II Forked light barrier, infra-red Timer box Multicore cable, 6-pole, 1.5 m long Sensor CASSY CASSY Lab additionally required: 1 PC with Windows 95/NT or higher 1 1 2 1 2 1 1 1 Torsion impacts between rotating bodies can be described analogously to one-dimensional translational collisions when the axes of rotation of the bodies are parallel to each other and remain unchanged during the collision. This condition is reliably met when carrying out measurements using the rotation model. The angular momentum is specified in the form L=l · v I: moment of inertia, v: angular velocity. The principle of conservation of angular momentum states that for any torsion impact of two rotating bodies, the quantity L = l 1 v1 + l 2 · v2 before and after impact remains the same. The two experiments investigate the nature of elastic and inelastic torsion impact. Using two forked light barriers and the computer-assisted measuring system CASSY, the obscuration times of two interrupter flags are registered as a measure of the angular velocities before and after torsion impact. The CASSY Lab uses the obscuration times Dt and the angular field Df = 10° of the interrupter flags to calculate the angular velocities 10° v= Dt as well as the angular momentums and energies before and after impact. P 1.4.2.1-2 35 Rotational motions of a rigid body P 1.4.3 Centrifugal force Mechanics P 1.4.3.1 Centrifugal force on a revolving body - measuring with the centrifugal force apparatus Centrifugal force on a revolving body - measuring with the centrifugal force apparatus (P 1.4.3.1) To measure the centrifugal force F = m · v2 · r a body with the mass m is caused to move in the centrifugal force apparatus with the angular velocity v along an arc with the radius r. The body is attached to a mirror elastically mounted above the axis of rotation via a wire. The centrifugal force tilts the mirror, whereby the change in the arc radius caused by this tilt is negligible. The tilt is proportional to the centrifugal force and can be detected using a light pointer. The arrangement is calibrated using a precision dynamometer while the centrifugal force apparatus is idle. In this experiment the centrifugal force F is determined as a function of the angular velocity v for two different radii r and two different masses m. The angular velocity is determined from the orbit period T of the light pointer, which is measured manually using a stopclock. This experiment verifies the relationship F “ v2, F “ m and F “ r. Cat. No. 347 22 347 35 347 36 450 51 450 60 460 20 521 210 Description Centrifugal force apparatus Experiment motor Control unit for experiment motor Lamp, 6 V/30 W Lamp housing Aspherical condenser Transformer, 6 V AC,12 V AC/30 VA Vertical scale, 1 m long Precision dynamometer, 1.0 N Stopclock I, 30 s / 15 min Stand base, V-shape, 20 cm 311 22 314 141 313 07 300 02 300 11 300 41 301 01 I Stand rod, 25 cm I Leybold multiclamp Saddle base I1 I1 Light pointer deflection s as a function of the square of the angular velocity v 36 P 1.4.3.1 1 1 1 1 1 1 1 1 1 1 1 1 Mechanics Rotational motions of a rigid body P 1.4.3. Centrifugal force P 1.4.3.2 Centrifugal force on a revolving body – measuring with the central force apparatus Centrifugal force on a revolving body – measuring with the central force apparatus (P 1.4.3.2) Cat. No. 347 21 314 251 501 16 521 35 337 41 575 664 301 06 501 46 Description Central force apparatus Newton meter Multicore cable, 6-pole, 1.5 m long Variable extra low voltage transformer S Tachymeter XY-Yt recorder Bench clamp Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 4 In the central force apparatus, the centrifugal force F = m · C2 · r r: radius of orbit, C: angular velocity is transmitted to a revolving body of the mass m by means of a system of angled levers and a needle bearing on a leaf spring with strain gauge. The transmission ratio of the lever system is selected so that the change in the orbit radius r for the revolving body is negligible. The force exerted on the strain gauge is measured using a newton meter; its analog output signal is led out to the Y-input of an XY recorder. A tachometer connected to the central force apparatus measures the angular velocity and generates an analog signal which is fed into the X-input of the recorder. In this experiment, the relationship F “ C2 is derived directly from the parabolic shape of the recorder curve. To verify the proportionalities F “ r and F “ m the curves are recorded for different orbit radii r and various masses m. Centrifugal force F as a function of the angular velocity C P 1.4.3.2 37 Rotational motions of a rigid body P 1.4.4 Motions of a gyroscope Mechanics P 1.4.4.1 Precession of a gyroscope P 1.4.4.2 Nutation of a gyroscope Precession of a gyroscope (P 1.4.4.1) Gyroscopes generally execute extremely complex motions, as the axis of rotation is supported at only one point and changes directions constantly. We distinguish between the precession and the nutation of a gyroscope. The aim of the first experiment is to investigate the precession of a symmetrical gyroscope which is not supported at its center of gravity. A forked light barrier and a digital counter are used to measure the precession frequency fp of the axis of symmetry around the fixed vertical axis for different distances d between the resting point and the center of gravity as a function of the frequency f with which the gyroscope rotates on its axis of symmetry. This experiment quantatively verifies the relationship d·G CP = I· C which applies for the corresponding angular frequencies CP and C and for a known weight G and known moment of inertia I of the gyroscope around its axis of symmetry. The second experiment takes a quantitative look at the nutation of a force-free gyroscope supported at its center of gravity. Here, the aim is to measure the nutation frequency fN of the axis of symmetry around the axis of angular momentum, which is fixed in space, as a function of the frequency f with which the gyroscope turns on its axis of symmetry. The aim of the evaluation is to verify the relationship which applies for small angles between the axis of angular momentum and the axis of symmetry: I·C CN = ID To achieve this, an additional measurement is carried out to record not only the principle moment of inertia I around the axis of symmetry, but also the principle moment of inertia ID around the axis perpendicular to it. Cat. No. Description 348 18 575 48 337 46 501 16 300 02 301 07 300 43 300 41 301 01 590 24 311 52 314 201 Large gyroscope Digital counter Forked light barrier, infra-red Multicore cable, 6-pole, 1.5 m Stand base, V-shape, 20 cm Simple bench clamp Stand rod, 75 cm Stand rod, 25 cm Leybold multiclamp Set of 10 load pieces, 100 g each Vernier calipers, plastic Precision dynamometer 100.0 N P 1.4.4.1 P 1.4.4.2 Precession (left) and nutation (right) of a gyroscope. (d: axis of figure, L: axis of angular momentum, C: instantaneous axis of rotation) 38 P 1.4.4.1-2 1 1 2 2 1 1 1 1 1 1 1 1 Mechanics Rotational motions of a rigid body P 1.4.5 Moment of inertia P 1.4.5.1 Definition of moment of inertia P 1.4.5.2 Moment of inertia and body shape P 1.4.5.3 Steiner’s law Definition of moment of inertia (P 1.4.5.1) Cat. No. 347 80 347 81 347 82 347 83 313 07 314 141 300 02 Description Torsion axle Set of cyliders for torsion axle Ball for torsion axle Circular disc for torsion axle Stopclock I 30 s/15 min Precision dynamometer, 1.0 N Stand base, V-shape, 20 cm For any rigid body whose mass elements mi are at a distance of ri from the axis of rotation, the moment of inertia is l = S m i · r i2 i P 1.4.5.2 1 1 1 P 1.4.5.1 1 P 1.4.5.3 1 1 1 1 1 1 1 1 1 1 1 For a particle of mass m in an orbit with the radius r, we can say l = m · r 2. The moment of inertia is determined from the oscillation period of the torsion axle on which the test body is mounted and which is elastically joined to the stand via a helical spring. The system is excited to harmonic oscillations. For a known directed angular quantity D, the oscillation period T can be used to calculate the moment of inertia of the test body using the equation T 2. l=D· 2ö ( ) Steiner's law (P 1.4.5.3) In the first experiment, the moment of inertia of a ”mass point” is determined as a function of the distance r from the axis of rotation. In this experiment, a rod with two weights of equal mass is mounted transversely on the torsion axle. The centers of gravity of the two weights have the same distance r from the axis of rotation, so that the system oscillates with no unbalanced weight. The second experiment compares the moments of inertia of a hollow cylinder, a solid cylinder and a solid sphere. This measurement uses two solid cylinders with equal mass but different radii. Additionally, this experiment examines a hollow cylinder which is equal to one of the solid cylinders in mass and radius, as well as a solid sphere with the same moment of inertia as one of the solid cylinders. The third experiment verifies Steiner’s law using a flat circular disk. Here, the moments of inertia IA of the circular disk are measured for various distances a from the axis of rotation, and compared with the moment of inertia Is around the axis of the center of gravity. This experiment confirms the relationship IA – IS = M · a2 39 Oscillations P 1.5.1 Mathematic and physical pendulum P 1.5.1.1 Determining the gravitational acceleration with a mathematic pendulum P 1.5.1.2 Determining the gravitational acceleration with a reversible pendulum Mechanics Determining the gravitational acceleration with a mathematic pendulum (P 1.5.1.1) Determining the gravitational acceleration with a reversible pendulum (P 1.5.1.2) P 1.5.1.2 1 1 1 1 1 P 1.5.1.1 1 A simple, or “mathematic” pendulum is understood to be a pointshaped mass m suspended on a massless thread with the length s. For small deflections, it oscillates under the influence of gravity with the period s T = 2ö · g Cat. No. 346 39 346 111 311 77 313 07 Description Ball with pendulum suspension Reversible pendulum Steel tape measure, 2 m Stopclock I 30 s / 15 min ö Thus, a mathematic pendulum could theoretically be used to determine the gravitational acceleration g precisely through measurement of the oscillation period and the pendulum length. In the first experiment, the ball with pendulum suspension is used to determine the gravitational acceleration. As the mass of the ball is much greater than that of the steel wire on which it is suspended, this pendulum can be considered to be a close approximation of a mathematic pendulum. Multiple oscillations are recorded to improve measuring accuracy. For gravitational acceleration, the error then depends essentially on the accuracy with which the length of the pendulum is determined. The reversible pendulum used in the second experiment has two edges for suspending the pendulum and two sliding weights for “tuning” the oscillation period. When the pendulum is properly adjusted, it oscillates on both edges with the same period sred T0 = 2ö · g ö and the reduced pendulum length sred corresponds to the very precisely known distance d between the two edges. For gravitational acceleration, the error then depends essentially on the accuracy with which the oscillation period T0 is determined. Measurement diagram for reversible pendulum (P 1.5.1.2) 40 Mechanics Oscillations P 1.5.2 Harmonic oscillations P 1.5.2.1 Oscillation of a spring pendulum – recording path, velocity and acceleration with CASSY P 1.5.2.2 Dependency of the oscillation period of a spring pendulum on the oscillating mass Oscillation of a spring pendulum – recording path, velocity and acceleration with CASSY (P 1.5.2.1) Cat. No. Description 352 10 342 61 336 21 337 631 524 032 501 16 524 010 524 200 300 01 300 41 300 46 301 01 301 08 309 48 501 46 Helical spring, 2 N, 0.03 N/cm Set of 12 weights, 50 g each Holding magnet with clamp Motion sensing element Motion transducer box Multicore cable, 6-pole, 1.5 m long Sensor CASSY CASSY Lab Stand base, V-shape, 28 cm Stand rod, 25 cm Stand rod, 150 cm Leybold multiclamp Clamp with hook Cord, 10 m Pair of cables, 1 m, red and blue additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 When a system is deflected from a stable equilibrium position, oscillations can occur. An oscillation is considered harmonic when the restoring force F is proportional to the deflection x from the equilibrium position. F=D·x D: directional constant The oscillations of a spring pendulum are often used as a classic example of this. In the first experiment, the harmonic oscillations of a spring pendulum are recorded as a function of time using the motion transducer and the computer-assisted measured value recording system CASSY. In the evaluation, the oscillation quantities path x, velocity v and acceleration a are compared on the screen. These can be displayed either as functions of the time t or as a phase diagram. The second experiment records and evaluates the oscillations of a spring pendulum for various suspended masses m. The relationship D T = 2ö · m P 1.5.2.1-2 ö for the oscillation period is verified. 41 Oscillations P 1.5.3 Torsion pendulum Mechanics P 1.5.3.1 Free rotational oscillations – measuring with a hand-held stopclock P 1.5.3.2 Forced rotational oscillations – measuring with a hand-held stopclock Forced rotational oscillations – measuring with a hand-held stopclock (P 1.5.3.2) The torsion pendulum after Pohl can be used to investigate free or forced harmonic rotational oscillations. An electromagnetic eddy current brake damps these oscillations to a greater or lesser extent, depending on the set current. The torsion pendulum is excited to forced oscillations by means of a motor-driven eccentric rod. The aim of the first experiment is to investigate free harmonic rotational oscillations of the type f(t) = f0 · cosvt · e–d · t where v = öv2 – d2 0 v0: characteristic frequency of torsion pendulum To distinguish between oscillation and creepage, the damping constant F is varied to find the current I0 which corresponds to the aperiodic limiting case. In the oscillation case, the angular frequency v is determined for various damping levels from the oscillation period T and the damping constant d by means of the ratio fn +1 T = e– d · 2 fn of two sequential oscillation amplitudes. Using the relationship v2 = v2 – d2 0 we can determine the characteristic frequency v0. In the second experiment, the torsion pendulum is excited to oscillations with the frequency v by means of a harmonically variable angular momentum. To illustrate the resonance behavior, the oscillation amplitudes determined for various damping levels are plotted as a function of v2 and compared with the theoretical curve M 1 f0 = 0 · I ö(v2 – v2 )2 + d2 · v2 0 Cat. No. 346 00 346 012 531 100 531 100 313 07 500 442 501 46 Description Torsion pendulum Torsion pendulum power supply Amperemeter, DC, I ≤ 2 A, e.g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 24 V, e. g. Multimeter METRAmax 2 Stopclock I 30 s/15 min Connection lead, 100 cm, blue Pair of cables, 1 m, red and blue 1 1 1 1 1 1 I: moment of inertia of torsion pendulum (cf. diagram). Resonance curves for two different damping constants 42 P 1.5.3.2 1 1 1 1 1 1 3 P 1.5.3.1 Mechanics Oscillations P 1.5.3 Torsion pendulum P 1.5.3.3 Free rotational oscillations – recording with CASSY P 1.5.3.4 Forced harmonic and chaotic rotational oscillations – recording with CASSY Chaotic rotational oscillations – recording with CASSY (P 1.5.3.4) Cat. No. Description 346 00 346 012 337 631 524 032 501 16 524 010 524 200 531 100 531 100 301 07 500 442 501 46 Torsion pendulum Torsion pendulum power supply Motion transducer BMW box Multicore cable, 6-pole, 1.5 m Sensor CASSY CASSY Lab Ammeter, DC, I ≤ 2 A, e.g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 24 V, e.g. Multimeter METRAmax 2 Simple bench clamp Connecting lead, blue, 100 cm Pair of cables, 100 cm, red and blue additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The computer-assisted CASSY measured-value recording system is ideal for recording and evaluating the oscillations of the torsion pendulum. The numerous evaluation options enable a comprehensive comparison between theory and experiment. Thus, for example, the recorded data can be displayed as pathtime, velocity-time and acceleration-time diagrams or as a phase diagram (path-velocity diagram). The aim of the first experiment is to investigate free harmonic rotational oscillations of the general type . f(t) = (f(0) · cosvt + G (0) · sinvt) · e-ut where v = ß v 2 – u2 0 v0 : characteristic frequency of torsion pendulum This experiment investigates the relationship between the initial deflection f(0) and the initial velocity v(0). In addition, the damping constant u is varied in order to find the current l0 which corresponds to the aperiodic limiting case. To investigate the transition between forced harmonic and chaotic oscillations, the linear restoring moment acting on the torsion pendulum is deliberately altered in the second experiment by attaching an additional weight to the pendulum. The restoring moment now corresponds to a potential with two minima, i.e. two equilibrium positions. When the pendulum is excited at a constant frequency, it can oscillate around the left minimum, the right minimum or back and forth between the two minima. At certain frequencies, it is not possible to predict when the pendulum will change from one minimum to another. The torsion pendulum is then oscillating in a chaotic manner. 1 1 1 1 Potential energy of double pendulums with and without additional mass P 5.2.1.2 P 1.5.3.4 1 1 3 1 P 5.2.1.1 P 1.5.3.3 43 Oscillations P 1.5.4 Coupling of oscillations Mechanics P 1.5.4.1 Coupled pendulums – measuring with a hand-held stopclock P1.5.4.2 Coupled pendulums – measuring and evaluating with VideoCom Coupled pendulums – measuring with a hand-held stopclock (P 1.5.4.1) Two coupled pendulums oscillate in phase with the angular frequency v+ when they are deflected from the equilibrium position by the same amount. When the second pendulum is deflected in the opposite direction, the two pendulums oscillate in phase opposition with the angular frequency v–. Deflecting only one pendulum generates a coupled oscillation with the angular frequency v + v– v= + 2 in which the oscillation energy is transferred back and forth between the two pendulums. The first pendulum comes to rest after a certain time, while the second pendulum simultaneously reaches its greatest amplitude. Then the same process runs in reverse. The time from one pendulum stand still to the next is called the beat period Ts. For the corresponding beat frequency, we can say vs = v+ – v– The aim of the first experiment is to observe in-phase, phaseopposed and coupled oscillations. The angular frequencies v+, v–, vs and v are calculated from the oscillation periods T+, T-, TS and T measured using a stopclock and compared with each other. In the second experiment, the coupled motion of the two pendulums is investigated using the single-line CCD camera VideoCom. The results include the path-time diagrams s1(t) and s2(t) of pendulums 1 and 2, from which the path-time diagrams s+(t) = s1(t) + s2(t) of the purely in-phase motion and und s-(t) = s1(t) – s2(t) of the purely opposed-phase motion are calculated. The corresponding characteristic frequencies are determined using Fourier transforms. Comparison identifies the two characteristic frequencies of the coupled oscillations s1(t) and s2(t) as the characteristic frequencies v+ of the function s+(t) and v+ of the function s-(t). Cat. No. 346 45 337 47 Description Double pendulum VideoCom 1 300 59 460 97 313 07 300 02 300 42 300 44 301 01 309 48 Tripod Scaled metal rail, 0.5 m Stopclock I, 30 s / 15 min Stand base, V-shape, 20 cm Stand rod, 47 cm Stand rod, 100 cm Leybold multiclamp Cord, 10 m additionally required: 1 PC with Windows 95 or Windows NT 1 1 2 1 2 4 1 Phase shift of the coupled oscillation – recorded with VideoCom (P 1.5.4.2) 44 P 1.5.4.2 1 1 1 1 2 1 2 4 1 1 P 1.5.4.1 Mechanics Oscillations P 1.5.4 Coupling of oscillations P 1.5.4.3 Coupling of longitudinal and rotational oscillations with Wilberforce’s pendulum Coupling of longitudinal and rotational oscillations with Wilberforce’s pendulum (P 1.5.4.3) Cat. No. 346 51 311 22 300 11 313 17 Description Wilberforce's pendulum Vertical scale, 1 m long Saddle base Stopclock II 60 s/30 min 1 1 1 1 Wilberforce’s pendulum is an arrangement for demonstrating coupled longitudinal and rotational oscillations. When a helical spring is elongated, it is always twisted somewhat as well. Therefore, longitudinal oscillations of the helical screw always excite rotational oscillations also. By the same token, the rotational oscillations generate longitudinal oscillations, as torsion always alters the spring length somewhat. The characteristic frequency fr of the longitudinal oscillation is determined by the mass m of the suspended metal cylinder, while the characteristic frequency fR of the rotational oscillation is established by the moment of inertia I of the metal cylinder. By mounting screwable metal disks on radially arranged threaded pins, it becomes possible to change the moment of inertia I without altering the mass m. The first step in this experiment is to match the two frequencies fT und fR by varying the moment of inertia I. To test this condition, the metal cylinder is turned one full turn around its own axis and raised 10 cm at the same time. When the frequencies have been properly matched, this body executes both longitudinal and rotational oscillations which do not affect each other. Once this has been done, it is possible to observe for any deflection how the longitudinal and rotational oscillations alternately come to a standstill. In other words, the system behaves like two classical coupled pendulums. P 1.5.4.3 45 Wave mechanics P 1.6.1 Transversal and longitudinal waves P 1.6.1.1 Standing transversal waves on a string P 1.6.1.2 Standing longitudinal waves on a helical spring Mechanics Standing transversal waves on a string (P 1.6.1.1) Standing longitudinal waves on a helical spring (P 1.6.1.2) A wave is formed when two coupled, oscillating systems sequentially execute oscillations of the same type. The wave can be excited e.g. as a transversal wave on an elastic string or as a longitudinal wave along a helical spring. The propagation velocity of an oscillation state — the phase velocity v — is related to the oscillation frequency f and the wavelength l through the formula v=l·f When the string or the helical spring is fixed at both ends, reflections occur at the ends. This causes superposing of the “outgoing” and reflected waves. Depending on the string length s, there are certain frequencies at which this superposing of the waves forms stationary oscillation patterns – standing waves. The distance between two oscillation nodes or two antinodes of a standing wave corresponds to one half the wavelength. The fixed ends correspond to oscillation nodes. For a standing wave with n oscillation antinodes, we can say l s=n· n . 2 This standing wave is excited with the frequency v . fn = n · 2s The first experiment examines standing string waves, while the second experiment looks at standing waves on a helical spring. In both cases, the relationship fn “ n is verified. Two helical springs with different phase velocities v are provided for use. Cat. No. Description 20066 629 Rubber band 352 07 352 08 579 42 522 621 1 Helical spring, 5 N, 0.1 N/cm Helical spring, 5 N, 0.25 N/cm STE motor with rocker Function generator S 12, 0.1 Hz to 20 kHz 1 1 311 78 301 21 301 26 301 27 301 25 666 615 301 29 314 04 501 46 Tape measure, 1.5m / 1 mm Stand base MF Stand rod, 25 cm, 10 mm dia. Stand rod, 50 cm, 10 mm dia. Clamping block MF Universal bosshead, 28 mm dia., 50 mm Pair of pointers Support clip, for plugging in Pair of cables, 1 m, red and blue 1 2 1 2 1 1 1 1 1 46 P 1.6.1.2 1 1 1 1 1 1 2 1 1 1 1 1 1 P 1.6.1.1 Mechanics Wave mechanics P 1.6.2 Wave machine P 1.6.2.1 Wavelength, frequency and phase velocity for travelling waves Wavelength, frequency and phase velocity for travelling waves (P 1.6.2.1) Cat. No. 401 20 401 22 401 23 401 24 521 35 521 25 313 07 311 77 501 46 Description Modular wave machine, basic module 1 Drive module for modular wave machine Damping module for modular wave machine Brake unit for modular wave machine DC voltage source, U = 0 – 12 V, e. g. Variable extra low voltage transformer S Transformer 2 . . . . 12 V Stopclock I 30 s / 15 min Steel tape measure, 2 m Pair of cables, 1 m, red and blue 2 1 1 2 1 1 1 1 2 The “modular wave machine” equipment set enables us to set up a horizontal torsion wave machine, while allowing the size and complexity of the setup within the system to be configured as desired. The module consists of 21 pendulum bodies mounted on edge bearings in a rotating manner around a common axis. They are elastically coupled on both sides of the axis of rotation, so that the deflection of one pendulum propagates through the entire system in the form of a wave. The aim of this experiment is to explicitly confirm the relationship v=l·f between the wavelength l, the frequency f and the phase velocity v. A stopclock is used to measure the time t required for any wave phase to travel a given distance s for different wavelengths; these values are then used to calculate the phase velocity s v= t The wavelength is then “frozen” using the built-in brake, to permit measurement of the wavelength l. The frequency is determined from the oscillation period measured using the stopclock. When the recommended experiment configuration is used, it is possible to demonstrate all significant phenomena pertaining to the propagation of linear transversal waves. In particular, these include the excitation of standing waves by means of reflection at a fixed or loose end. Relationship between the frequency and the wavelength of a propagating wave P 1.6.2.1 47 Wave mechanics P 1.6.3 Circularly polarized waves Mechanics P 1.6.3.1 Investigating circularly polarized string waves in the experiment setup after Melde P 1.6.3.2 Determining the phase velocity of circularly polarized string waves in the experiment setup after Melde Investigating circularly polarized string waves in the experiment setup after Melde (P 1.6.3.1) The experiment setup after Melde generates circularly polarized string waves on a string with a known length s using a motordriven eccentric. The tensioning force F of the string is varied until standing waves with the wavelength 2s ln = n n: number of oscillation nodes appear. In the first experiment, the wavelengths ln of the standing string waves are determined for different string lengths s and string masses m at a fixed excitation frequency and plotted as a function of the respective tensioning force Fm. The evaluation confirms the relationship F l“ m* Cat. No. 401 03 311 77 451 281 315 05 Description Vibrating thread apparatus Steel tape measure, 2 m Stroboscope, 1. . . 330 Hz School and laboratory balance 311, 311 g 1 1 ö with the mass assignment m m* = s m: string mass, s: string length In the second experiment, the same measuring procedure is carried out, but with the addition of a stroboscope. This is used to determine the excitation frequency f of the motor. It also makes the circular polarization of the waves visible in an impressive manner when the standing string wave is illuminated with light flashes which have a frequency approximating that of the standard wave. The additional determination of the frequency f enables calculation of the phase velocity c of the string waves using the formula c=l·f as well as quantitative verification of the relationship F . c= m* ö 48 P 1.6.3.2 1 1 1 1 P 1.6.3.1 Mechanics Wave mechanics P 1.6.4 Propagation of water waves P 1.6.4.1 Generating circular and straight water waves P 1.6.4.2 Applying Huygens’ principle to water waves P 1.6.4.3 Propagation of water waves in two different depths P 1.6.4.4 Refraction of water waves P 1.6.4.5 Doppler effect in water waves P 1.6.4.6 Reflection of water waves at a straight obstacle P 1.6.4.7 Reflection of water waves at curved obstacles Generating circular water waves (P 1.6.4.1) Cat. No. Description 401 501 313 033 311 77 Wave trough with stroboscope Electronic stopclock P Steel tape measure, 2 m 1 1 1 1 1 1 1 Fundamental concepts of wave propagation can be explained particularly clearly using water waves, as their propagation can be observed with the naked eye. The first experiment investigates the properties of circular and straight waves. The wavelength Ö is measured as a function of each excitation frequency f and these two values are used to calculate the wave velocity v=f·Ö The aim of the second experiment is to verify Huygens’ principle. In this experiment, straight waves strike an edge, a narrow slit and a grating. We can observe a change in the direction of propagation, the creation of circular waves and the superposing of circular waves to form one straight wave. The third and fourth experiments aim to study the propagation of water waves in different water depths. A greater water depth corresponds to a medium with a lower refractive index n. At the transition from one “medium” to another, the law of refraction applies: sina1 Ö1 = sina2 Ö2 a1, a2: angles with respect to axis of incidence in zones 1 and 2 Ö1, Ö2: wavelength in zones 1 and 2 A prism, a biconvex lens and a biconcave lens are investigated as practical applications for water waves. The fifth experiment observes the Doppler effect in circular water waves for various speeds u of the wave exciter. The last two experiments examine the reflection of water waves. When straight and circular waves are reflected at a straight wall, the “wave beams” obey the law of reflection. When straight waves are reflected by curved obstacles, the originally parallel wave rays travel in either convergent or divergent directions, depending on the curvature of the obstacle. We can observe a focusing to a focal point, respectively a divergence from an apparent focal point, just as in optics. P 1.6.4.4-7 P 1.6.4.2 P 1.6.4.3 P 1.6.4.1 Convergent beam path behind a biconvex lens (P 1.6.4.4) 49 Wave mechanics P 1.6.5 Interference with water waves P 1.6.5.1 Two-beam interference of water waves P 1.6.5.2 Lloyd’s experiment using water waves P 1.6.5.3 Diffraction of water waves at a slit and an obstacle P 1.6.5.4 Diffraction of water waves at a multiple slit P 1.6.5.5 Generating standing waves in front of a reflecting barrier Mechanics Two-beam interference of water waves (P 1.6.5.1) Experiments on the interference of waves can be carried out in an easily understandable manner, as the diffraction objects can be seen and the propagation of the diffracted waves observed with the naked eye. In the first experiment, the interference of two coherent circular waves is compared with the diffraction of straight waves at a double slit. The two arrangements generate identical interference patterns. The second experiment reproduces Lloyd’s experiment on generating two-beam interference. A second wave coherent to the first is generated by reflection at a straight obstacle. The result is an interference pattern which is equivalent to that obtained for two-beam interference with two discrete coherent exciters. In the third experiment, a straight wave front strikes slits and obstacles of various widths. A slit which has a width of less than the wavelength acts like a point-shaped exciter for circular waves. If the slit width is significantly greater than the wavelength, the straight waves pass the slit essentially unaltered. Weaker, circular waves only propagate in the shadow zones behind the edges. When the slit widths are close to the wavelength, a clear diffraction pattern is formed with a broad main maximum flanked by lateral secondary maxima. When the waves strike an obstacle, the two edges of the obstacle act like excitation centers for circular waves. The resulting diffraction pattern depends greatly on the width of the obstacle. The object of the fourth experiment is to investigate the diffraction of straight water waves at double, triple and multiple slits which have a fixed slit spacing d. This experiment shows that the diffraction maxima become more clearly defined for an increasing number n of slits. The angles at which the diffraction maxima are located remain the same. P 1.6.5.1-4 1 Cat. No. 401 501 311 77 Description Wave trough with stroboscope Steel tape measure, 2 m The last experiment demonstrates the generation of standing waves by means of reflection of water waves at a wall arranged parallel to the wave exciter. The standing wave demonstrates points at regular intervals at which the crests and troughs of the individual traveling and reflected waves cancel each other out. The oscillation is always greatest at the midpoint between two such nodes. Diffraction of water waves at a narrow obstacle (P 1.6.5.3) 50 P 1.6.5.5 1 1 Mechanics P 1.7.1 Sound waves Acoustics P 1.7.1.1 P 1.7.1.2 P 1.7.1.3 Mechanical oscillations and sound waves using the recording tuning fork Acoustic beats – display on the oscilloscope Acoustic beats – recording with CASSY Acoustic beats – recording with CASSY (P 1.7.1.3) Cat. No. 414 76 459 32 414 72 586 26 575 211 575 35 524 010 524 200 300 11 Description Recording tuning fork, 128 Hz Set of 20 candles Pair of resonance tuning forks, 440 Hz Multi-purpose microphone Two-channel oscilloscope 303 BNC/4 mm adapter, 2-pole Sensor-CASSY CASSY Lab Saddle base 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 additionally recommended: 1 PC with Windows 95 / NT or higher 1 Acoustics is the study of sound and all its phenomena. This discipline deals with both the generation and the propagation of sound waves. The object of the first experiment is the generation of sound waves by means of mechanical oscillations. The mechanical oscillations of a tuning fork are recorded on a glass plate coated with carbon black. At the same time the sound waves are registered using a microphone and displayed on an oscilloscope. The recorded signals are the same shape; fundamental oscillations and harmonics are visible in both cases. The second experiment demonstrates the wave nature of sound. Here, acoustic beats are investigated as the superposing of two sound waves generated using tuning forks with slightly different frequencies f1 and f2. The beat signal is received via a microphone and displayed on the oscilloscope. By means of further (mis-) tuning of one tuning fork by moving a clamping screw, the beat frequency fS = f2 – f1 is increased, and the beat period (i. e. the interval between two nodes of the beat signal) 1 TS = fS is reduced. In the third experiment, the acoustic beats are recorded and evaluated via the CASSY computer interface device. The individual frequencies f1 and f2, the oscillation frequency f and the beat frequency fS are determined automatically and compared with the calculated values f + f2 f= 1 2 fS = f2 – f1. P 1.7.1.2 Mechanical oscillations and sound waves using the recording tuning fork (P 1.7.1.1) P 1.7.1.3 P 1.7.1.1 51 Acoustics P 1.7.2 Oscillations of a string Mechanics P 1.7.2.1 Determining the oscillation frequency of a string as a function of the string length and tensile force Determining the oscillation frequency of a string as a function of the string length and tensile force (P 1.7.2.1) In the fundamental oscillation, the string length s of an oscillating string corresponds to half the wavelength. Therefore, the following applies for the frequency of the fundamental oscillation: c f= , 2s where the phase velocity c of the string is given by c= Cat. No. 414 01 314 201 524 010 524 034 Description Monochord Precision dynamometer 100.0 N Sensor CASSY Timer box Forked light barrier, infra-red Multicore cable, 6-pole, 1.5 m long CASSY Lab Stand base, V-shape, 20 cm Stand rod, 10 cm Stand rod, 25 cm Leybold multiclamp additionally required: 1 PC with Windows 95/NT or higher ö F A·r 337 46 501 16 524 200 300 02 300 40 300 41 301 01 F: tensioning force, A: area of cross-section, r: density In this experiment, the oscillation frequency of a string is determined as a function of the string length and tensioning force. The measurement is carried out using a forked light barrier and the computer-assisted measuring system CASSY, which is used here as a high-resolution stop-clock. The aim of the evaluation is to verify the relationships 1 f “ öF and f “ . s Frequency f as a function of the string length s 52 P 1.7.2.1 1 1 1 1 1 1 1 1 1 1 1 1 Mechanics Acoustics P 1.7.3 Wavelength and velocity of sound P 1.7.3.1 Kundt’s tube: determining the wavelength using the cork-powder method Determining the wavelength of standing sound waves P 1.7.3.2 Kundt’s tube: determining the wavelength using the cork-powder method (P 1.7.3.1) Cat. No. 413 01 586 26 587 08 587 66 522 621 Description Kundt's tube Multi-purpose microphone Broad-band speaker Reflection plate Function generator S 12, 0.1 Hz to 20 kHz, supply: 12 V DC Voltmeter, DC, U ≤ 3 V, e. g. Multimeter METRAmax 2 Steel tape measure, 2m Scaled metal rail, 0.5 m Saddle base 1 1 1 1 1 Just like other waves, reflection of sound waves can produce standing waves in which the oscillation nodes are spaced at l d= 2 Thus, the wavelength l of sound waves can be easily measured at standing waves. The first experiment investigates standing waves in Kundt’s tube. These standing waves are revealed in the tube using cork powder which is stirred up in the oscillation nodes. The distance between the oscillation nodes is used to determine the wavelength l. In the second experiment, standing sound waves are generated by reflection at a barrier. This setup uses a function generator and a loudspeaker to generate sound waves in the entire audible range. A microphone is used to detect the intensity minima, and the wavelength b is determined from their spacings. 531 100 311 77 460 97 300 11 501 46 1 Pair of cables, 1 m, red and blue P 1.7.3.2 1 1 P 1.7.3.1 3 1 Determining the wavelength of standing sound waves (P 1.7.3.2) 53 Acoustics P 1.7.3 Wavelength and velocity of sound P 1.7.3.3 Determining the velocity of sound in the air as a function of the temperature Determining the velocity of sound in gases Mechanics P 1.7.3.4 Determining the velocity of sound in the air as a function of the temperature (P 1.7.3.3) Sound waves demonstrate only slight dispersion, i.e. group and phase velocities demonstrate close agreement for propagation in gases. Therefore, we can determine the velocity of sound c as simply the propagation speed of a sonic pulse. In ideal gases, we can say p·k C c= where k = p r CV P 1.7.3.3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 Cat. No. 413 60 516 249 587 08 586 26 521 25 576 89 503 11 524 010 524 200 524 045 524 034 666 193 460 97 300 11 660 999 660 984 660 985 660 980 667 194 500 422 501 44 501 46 Description Apparatus for sound and velocity Stand for coils and tubes Broad-band speaker Multi-purpose microphone Transformer 2....12 V Battery case 2 x 4.5 volts Set of 20 batteries 1.5 V (type MONO) Sensor CASSY CASSY Lab Temperature box Timer box Temperature sensor, NiCr-Ni Scaled metal rail, 0.5 m Saddle base Minican gas can, carbon dioxide Minican gas can, helium Minican gas can, neon Fine regulating valve for Minican gas cans Silicone tubing, i.d. 7 x 1.5 mm, 1 m Connection lead, blue, 50 cm Pair of cables, 25 cm, red and blue Pair of cables, 100 cm, red and blue additionally required: 1 PC with Windows 95/NT or higher ö p: pressure, r: density, k: adiabatic coefficient Cp, CV: specific heat capacities The first experiment measures the velocity of sound in the air as a function of the temperature P and compares it with the linear function resulting from the temperature-dependency of pressure and density 1 a c(P) = c(0) · 1 + · P where a = 2 273 K ( ) The value c(0) determined using a best-fit straight line and the literature values p(0) and r(0) are used to determine the adiabatic coefficient k of air according to the formula c(0)2 · r(0) k= p(0) The second experiment determines the velocity of sound c in carbon dioxide and in the inert gases helium and neon. The evaluation demonstrates that the great differences in the velocities of sound of gases are essentially due to the different densities of the gases. The differences in the adiabatic coefficients of the gases are comparatively small. 54 P 1.7.3.4 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 Mechanics Acoustics P 1.7.3 Wavelength and velocity of sound P 1.7.3.5 Determining the velocity of sound in solid bodies Determining the velocity of sound in solid bodies (P 1.7.3.5) Cat. No. 413 65 300 46 587 25 524 010 524 200 301 07 501 38 Description Set of 3 metal rods, 1.5 cm Stand rod, 150 cm Rochelle salt crystal Sensor CASSY CASSY Lab Simple bench clamp Connecting lead 200 cm, black, Ø 2.5 mm2 additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 2 1 In solid bodies, the velocity of sound is determined by the modulus of elasticity E and the density r. For the velocity of sound in a long rod, we can say E c= r P 1.7.3.5 ö In the case of solids, measurement of the velocity of sound thus yields a simple method for determining the modulus of elasticity. The object of this experiment is to determine the velocity of sound in aluminum, copper, brass and steel rods. This measurement exploits the multiple reflections of a brief sound pulse at the rod ends. The pulse is generated by striking the top end of the rod with a hammer, and initially travels to the bottom. The pulse is reflected several times in succession at the two ends of the rod, whereby the pulses arriving at one end are delayed with respect to each other by the time Dt required to travel out and back. The velocity of sound is thus 2s c= Dt s: length of rod To record the pulses, the bottom end of the rod rests on a piezoelectric element which converts the compressive oscillations of the sound pulse into electrical oscillations. These values are recorded using the CASSY system for computer-assisted measured-value recording. CASSY can be used here either as a storage oscilloscope or as a high-resolution stopclock which is started and stopped by the edges of the voltage pulses. 55 Acoustics P 1.7.4 Reflection of ultrasonic waves P 1.7.4.1 P 1.7.4.2 Reflection of flat ultrasonic waves at a plane surface Principle of an echo sounder Mechanics Reflection of flat ultrasonic waves at a plane surface (P 1.7.4.1) When investigating ultrasonic waves, identical, and thus interchangeable transducers are used as transmitters and receivers. The ultrasonic waves are generated by the mechanical oscillations of a piezoelectric body in the transducer. By the same token, ultrasonic waves excite mechanical oscillations in the piezoelectric body. The aim of the first experiment is to confirm the law of reflection “angle of incidence = angle of reflection” for ultrasonic waves. In this setup, an ultrasonic transducer as a point-type source is set up in the focal point of a concave reflector, so that flat ultrasonic waves are generated. The flat wave strikes a plane surface at an angle of incidence a and is reflected there. The reflected intensity is measured at different angles using a second transducer. The direction of the maximum reflected intensity is defined as the angle of reflection b. The second experiment utilizes the principle of an echo sounder to determine the velocity of sound in the air, as well as to determine distances. An echo sounder emits pulsed ultrasonic signals and measures the time at which the signal reflected at the Cat. No. 416 000 416 014 416 013 389 241 416 020 587 66 575 211 575 24 460 43 460 40 300 01 300 02 300 11 300 41 300 42 301 01 301 27 311 02 311 77 361 03 Description Ultrasonic transducer 40 kHz Generator 40 kHz AC amplifier Concave mirror, dia. 39 cm Sensor holder for concave mirror Reflection plate 50 x 50 cm Two-channel oscilloscope 303 Screened cable BNC/4 mm Small optical bench Swivel joint with angle scale Stand base, V-shape, 28 cm Stand base, V-shape, 20 cm Saddle base Stand rod, 25 cm Stand rod, 47 cm Leybold multiclamp Stand rod, 50 cm, 10 mm dia. Metal scale, 1 m long Steel tape measure, 2 m Spirit level 2 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 boundary surface is received. For the sake of simplicity, the transmitter and receiver are set up as nearly as possible in the same place. When the velocity of sound c is known, the time difference t between transmission and reception can be used in the relationship 2s c= t Principle of an echo sounder (P 1.7.4.2) to determine the distance s to the reflector or, when the distance is known, the velocity of sound. 56 P 1.7.4.2 2 1 1 1 1 2 3 P 1.7.4.1 Mechanics P 1.7.5 Interference of ultrasonic waves P 1.7.5.1 P 1.7.5.2 P 1.7.5.3 P 1.7.5.4 Acoustics Beating of ultrasonic waves Interference of two ultrasonic beams Diffraction of ultrasonic waves at a single slit Diffraction of ultrasonic waves at a double slit, multiple slit and grating Diffraction of ultrasonic waves at a double slit, multiple slit and grating (P 1.7.5.4) Cat. No. 416 000 416 013 416 014 416 020 416 021 416 030 311 902 389 241 575 211 575 24 524 010 524 031 524 200 521 545 501 031 311 77 300 01 300 02 300 11 300 41 300 42 301 01 500 424 501 46 Description Ultrasonic transducer 40 kHz AC amplifier Generator 40 kHz Sensor holder for concave mirror Rack for diffraction objects Slit and grating for ultrasonic experiments Rotating platform with motor drive Concave mirror, dia. 39 cm Two-channel oscilloscope 303 Screened cable BNC/4 mm Sensor CASSY Current supply box CASSY Lab DC power supply, 0 ... 16 V/5 A Connecting lead, 8 m, screened Steel tape measure, 2 m Stand base, V-shape, 28 cm Stand base, V-shape, 20 cm Saddle base Stand rod, 25 cm Stand rod, 47 cm Leybold multiclamp Connection lead, 50 cm, blue Pair of cables, 100 cm, red and blue additionally required: 1 PC with Windows 95/98/NT 3 1 2 3 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Experiments on the interference of waves can be carried out in a comprehensible manner using ultrasonic waves, as the diffraction objects are visible with the naked eye. In addition, it is not difficult to generate coherent sound beams. In the first experiment, beating of ultrasonic waves is investigated using two transducers which are operated using slightly different frequencies f1 and f2. The signal resulting from the superposing of the two individual signals is interpreted as an oscillation with the periodically varying amplitude A(t) “ cos(ö · (f2 – f1) · t). The beat frequency fS determined from the period TS between two beat nodes and compared with the difference f2 – f1. In the second experiment, two identical ultrasonic transducers are operated by a single generator. These transducers generate two coherent ultrasonic beams which interfere with each other. The interference pattern corresponds to the diffraction of flat waves at a double slit when the two transducers are operated in phase. The measured intensity is thus greatest at the diffraction angles a where l sin a = n · where n = 0, ±1, ±2, ... d l: wavelength, d: spacing of ultrasonic transducers The last two experiments use an ultrasonic transducer as a point-shaped source in the focal point of a concave reflector. The flat ultrasonic waves generated in this manner are diffracted at a single slit, a double slit and a multiple slit. An ultrasonic transducer and the slit are mounted together on the turntable for computer-assisted recording of the diffraction figures. This configuration measures the diffraction at a single slit for various slit widths b and the diffraction at multiple slits and gratings for different numbers of slits N. P 1.7.5.2 P 1.7.5.3 P 1.7.5.4 P 1.7.5.1 57 Acoustics P 1.7.6 Acoustic Doppler effect Mechanics P 1.7.6.1 Investigating the Doppler effect with ultrasonic waves Investigating the Doppler effect with ultrasonic waves (P 1.7.6.1) The change in the observed frequency for a relative motion of the transmitter and receiver with respect to the propagation medium is called the acoustic Doppler effect. If the transmitter with the frequency f0 moves at a velocity v relative to a receiver at rest, the receiver measures the frequency f0 f= v where c: velocity of sound 1– c If, on the other hand, the receiver moves at a velocity v relative to a transmitter at rest, we can say v f = f0 · 1 + c Cat. No. 416 000 416 013 416 014 501 031 575 48 575 211 575 24 313 07 337 07 20066264 Description Ultrasonic transducer 40 kHz AC amplifier Generator 40 kHz Connecting lead, 8 m, screened Digital counter Two-channel oscilloscope 303 Screened cable BNC/4 mm Stopclock I, 30s/15min Trolley with electric drive Battery 1.5 V (type mignon cell) Precision metal rail, 1 m Rail connector Pair of feet Saddle base Stand rod, 25 cm Stand rod, 47 cm Leybold multiclamp Clamp with ring Set of 6 two-way adapters, black Pair of cables, 1 m, red and blue ( ) The change in the frequeny f – f0 is proportional to the frequency f0. Investigation of the acoustic Doppler effect on ultrasonic waves thus suggests itself. In this experiment, two identical ultrasonic transducers are used as the transmitter and the receiver, and differ only in their connection. One transducer is mounted on a measuring trolley with electric drive, while the other transducer is at rest on the lab bench. The frequency of the received signal is measured using a high-resolution digital counter. To determine the speed of the transducer in motion, the time Wt which the measuring trolley requires to traverse the measuring distance is measured using a stopclock. 460 81 460 85 460 88 300 11 300 41 300 42 301 01 301 10 501 644 501 46 The propagation of sound with the sound source and the observer at rest (left), with the sound source moving (middle), and with the observer moving (right) 58 P 1.7.6.1 2 1 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1 Mechanics P 1.7.7 Fourier analysis Acoustics P 1.7.7.1 P 1.7.7.2 P 1.7.7.3 P 1.7.7.4 Investigation of fast Fourier transforms: simulation of Fourier analysis and synthesis Fourier analysis of the periodic signals of a function generator Fourier analysis of an electrical oscillator circuit Fourier analysis of sounds Fourier analysis of sounds (P 1.7.7.4) Cat. No. 576 74 577 19 577 20 577 21 577 23 577 32 578 15 579 10 562 14 586 26 522 56 524 010 524 200 300 11 501 45 Description Plug-in board A4 STE resistor 1 V, 2 W STE resistor 10 V, 2 W STE resistor 5.1 V, 2 W STE resistor 20 V, 2 W STE resistor 100 V, 2 W STE capacitor 1 µF, 100 V STE key switch n.o., single pole Coil with 500 turns Multi-purpose microphone Function generator P, 100 mHz to 100 kHz Sensor CASSY CASSY Lab Saddle base Pair of cables, 50 cm, red and blue additionally recommended: 1 PC with Windows 95/NT or higher Fourier analysis and synthesis of sound waves are important tools in acoustics. Thus, for example, knowing the harmonics of a sound is important for artificial generation of sounds or speech. The first two experiments investigate Fourier transforms of periodic signals which are either numerically simulated or generated using a function generator. In the third experiment, the frequency spectrum of coupled electric oscillator circuits is compared with the spectrum of an uncoupled oscillator circuit. The Fourier transform of the uncoupled, damped oscillation is a Lorentz curve H2 , L(f) = L0 · (f – f0)2 + H2 in which the width increases with the ohmic resistance of the oscillator circuit. The Fourier-transformed signal of the coupled oscillator circuits shows the split into two distributions lying symmetrically around the uncoupled signal, with their spacing depending on the coupling of the oscillator circuits. The aim of the final experiment is to conduct Fourier analysis of sounds having different tone colors and pitches. As examples, the vowels of the human voice and the sounds of musical instruments are analyzed. The various vowels of a language differ mainly in the amplitudes of the harmonics. The fundamental frequency f0 depends on the pitch of the voice. This is approx. 200 Hz for high-pitched voices and approx. 80 Hz for low-pitched voices. The vocal tone color is determined by variations in the excitation of the harmonics. The audible tones of musical instruments are also determined by the excitation of harmonics. P 1.7.7.2 P 1.7.7.3 1 1 1 1 1 1 2 1 2 1 1 4 1 1 1 1 1 1 1 1 1 1 1 Fourier analysis of an electrical oscillator circuit (P 1.7.7.3) P 1.7.7.4 1 1 P 1.7.7.1 59 Aerodynamics and hydrodynamics P 1.8.1 Barometry Mechanics P 1.8.1.1 Definition of pressure P 1.8.1.2 Hydrostatic pressure as a nondirectional quantity Definition of pressure (P 1.8.1.1) p= F . A Cat. No. 361 30 375 58 590 24 300 02 300 42 361 57 Description Set of 2 gas syringes with holder Hand vacuum and pressure pump Set of 10 load pieces, 100 g each Stand base, V-shape, 20 cm Stand rod, 47 cm Liquid pressure gauge with U-tube manometer It is measurable as the distributed force F acting perpendicularly on an area A. The first experiment aims to illustrate the definition of pressure as the ratio of force and area by experimental means using two gas syringes of different diameters which are connected via a T-section and a hand pump. The pressure generated by the hand pump is the same in both gas syringes. Thus, we can say for the forces F1 and F2 acting on the gas syringes F1 A1 = F2 A2 A1, A2: cross-section areas The second experiment explores the hydrostatic pressure p=U·g·h U: density, g: gravitational acceleration in a water column subject to gravity. The pressure is measured as a function of the immersion depth h using a liquid pressure gauge. The displayed pressure remains constant when the gauge is turned in all directions at a constant depth. The pressure is thus a non-directional quantity. 1 1 1 1 1 1 311 77 361 575 I Steel tape measure, 2m Glass vessel for liquid pressure gauge I I1 Pressure-gauge reading as a function of the immersion depth (experiment P 1.8.1.2) Hydrostatic pressure as a nondirectional quantity (P 1.8.1.2) 60 P 1.8.1.2 1 P 1.8.1.1 In a gas or liquid at rest, the same pressure applies at all points: Mechanics Aerodynamics and hydrodynamics P 1.8.2 Buoyancy P 1.8.2.1 Confirming Archimedes’ principle P 1.8.2.2 Measuring the buoyancy as a function of the immersion depth Confirming Archimedes’ principle (P 1.8.2.1) Cat. No. 362 02 Description Archimedes cylinder Hydrostatic precision balance, 200 g Set of weights, 10 mg – 200 g Precision dynamometer, 1.0 N Steel tape measure, 2 m Beaker, 100 ml, ts, hard glass Beaker, 250 ml, ts, hard glass Glycerine, 99 %, 250 ml Ethanol, completely denaturated, 1 l 1 1 1 1 315 01 315 31 314 141 311 77 664 111 664 113 672 1210 671 9720 1 1 1 1 1 1 1 1 1 Archimedes’ principle states that the buoyancy force F acting on any immersed body corresponds to the weight G of the displaced liquid. The first experiment verifies Archimedes’ principle. In this experiment, a hollow cylinder and a solid cylinder which fits snugly inside it are suspended one beneath the other on the beam of a balance. The deflection of the balance is compensated to zero. When the solid cylinder is immersed in a liquid, the balance shows the reduction in weight due to the buoyancy of the body in the liquid. When the same liquid is filled in the hollow cylinder the deflection of the balance is once again compensated to zero, as the weight of the filled liquid compensates the buoyancy. In the second experiment, the solid cylinder is immersed in various liquids to the depth h and the weight G=r·g·A·h r: density, g: gravitational acceleration, A: cross-section of the displaced liquid is measured as the buoyancy F using a precision dynamometer. The experiment confirms the relationship F“r As long as the immersion depth is less than the height of the cylinder, we can say: F“h At greater immersion depths the buoyancy remains constant. P 1.8.2.2 P 1.8.2.1 61 Aerodynamics and hydrodynamics P 1.8.3 Viscosity Mechanics P 1.8.3.1 Assembling a falling-ball viscosimeter to determine the viscosity of viscous fluids P 1.8.3.2 Falling-ball viscosimeter: measuring the viscosity of sugar solutions as a function of the concentration P 1.8.3.3 Falling-ball viscosimeter: measuring the viscosity of Newtonian fluids as a function of the temperature Falling-ball viscosimeter after Höppner (P 1.8.3.2) The falling-ball viscometer is used to determine the viscosity of liquids by measuring the falling time of a ball. The substance under investigation is filled in the vertical tube of the viscosimeter, in which a ball falls through a calibrated distance of 100 mm. The resulting falling time t is a measure of the dynamic viscosity h of the liquid according to the equation J = K · (U1 – U2) · t U2: density of the liquid under study, whereby the constant K and the ball density U1 may be read from the test certificate of the viscosimeter. The object of the first experiment is to set up a falling-ball viscosimeter and to study this measuring method, using the viscosity of glycerine as an example. The second experiment investigates the relationship between viscosity and concentration using concentrated sugar solutions at room temperature. In the third experiment, the temperatureregulation chamber of the viscosimeter is connected to a circulation thermostat to measure the dependency of the viscosity of a Newtonian fluid (e. g. olive oil) on the temperature. P 1.8.3.2 1 1 Cat. No. 379 001 336 21 Description Guinea-and-feather apparatus Holding magnet with clamp 1 1 1 1 1 1 1 1 1 1 1 1 6 1 4 1* 1* 1* 1 1 1 200 67 288 Steel ball, 16 mm dia., for 371 05 504 52 521 230 575 451 Morse key Low-voltage power supply Counter P Pair of magnets, cylindrical Stand base, V-shape, 28 cm Stand rod, 100 cm Stand rod, 25 cm Leybold multiclamp Clamp with jaw clamp Glycerine, 99 %, 250 ml Pair of cables, 1 m, red and blue Connection lead, 50 cm, blue Measuring cylinder, 100 ml, plastic Precision vernier callipers Precision electronic balance LS 200, 200 g : 0.1 g Falling-ball viscosimeter C Stopclock I, 30 s/15 min Controlled-temperature recirculation unit, 30 ... 100°C 510 48 300 01 300 44 300 41 301 01 301 11 672 1210 501 46 500 422 590 08 311 54 667 793 665 906 313 07 666 768 667 194 i * additionally recommended I Steel tape measure, 2 m Silicone tubing, int. dia. 7 x 1.5 mm, 1 m I I I I1I I 311 77 62 P 1.8.3.3 2 P 1.8.3.1 Mechanics Aerodynamics and hydrodynamics P 1.8.4 Surface tension P 1.8.4.1 Measuring the surface tension using the tear-away method Measuring the surface tension using the tear-away method (P 1.8.4.1) Cat. No. 367 46 664 175 314 111 311 52 300 76 300 02 300 43 Description Apparatus for measuring surface tension Crystallization dish, 95 mm dia., height = 55 mm Precision dynamometer, 0.1 N Vernier callipers, plastic Laboratory stand II Stand base, V-shape, 20 cm Stand rod, 75 cm 1 1 1 1 1 1 1 1 301 08 671 9740 675 3400 Clamp with hook I I Ethanol, fully denaturated, 250 ml Water, pure, 1 l I1 I1 To determine the surface tension D of a liquid, a metal ring is suspended horizontally from a precision dynamometer. The metal ring is completely immersed in the liquid, so that the entire surface is wetted. The ring is then slowly pulled out of the liquid, drawing a thin sheet of liquid behind it. The liquid sheet tears when the tensile force exceeds a limit value F = s · 4S · R R: edge radius This experiment determines the surface tension of water and ethanol. It is shown that water has a particularly high surface tension in comparison to other liquids (literature value for water: 0.073 Nm-1, for ethanol: 0.022 Nm-1). P 1.8.4.1 63 Aerodynamics and hydrodynamics P 1.8.5 Introductory experiments in aerodynamics P 1.8.5.1 Static pressure in a reduced cross-section – measuring the pressure with the precision manometer P 1.8.5.2 Determining the volume flow with a Venturi tube – measuring the pressure with the precision manometer P 1.8.5.3 Determining the wind speed with a pressure head sensor – measuring the pressure with the precision manometer P 1.8.5.4 Static pressure in a reduced cross-section – measuring the pressure with a pressure sensor and CASSY P 1.8.5.5 Determining the volume flow with a Venturi tube – measuring the pressure with a pressure sensor and CASSY P 1.8.5.6 Determining the wind speed with a pressure head sensor – measuring the pressure with a pressure sensor and CASSY Mechanics Determining the volume flow with a Venturi tube – measuring the pressure with the precision manometer (P 1.8.5.2) The study of aerodynamics relies on describing the flow of air through a tube using the continuity equation and the Bernoulli equation. These state that regardless of the cross-section A of the tube, the volume flow . V=v ·A v: flow speed and the total pressure r p0 = p + pS where pS = · v 2 2 p: static pressure, pS: dynamic pressure, r: density of air remain constant as long as the flow speed remains below the speed of sound. In order to verify these two equations, the static pressure in a Venturi tube is measured for different cross-sections in the first experiment. The static pressure decreases in the reduced crosssection, as the flow speed increases here. The second experiment uses the Venturi tube to measure the volume flow. Using the pressure difference Dp = p2 - p1 between two points with known cross-sections A1 and A2, we obtain v1 · A1 = P 1.8.5.4 – 5 1 1 1 1 1 1 1 1 1 1 P 1.8.5.1–2 P 1.8.5.3 Cat. No. 373 04 373 09 373 10 373 13 524 010 524 066 Description Suction and pressure fan Venturi tube with 7 gauge points Precision manometer Pressure head Sensor CASSY Pressure sensor S, ± 70 hPa 1 1 1 1 1 1 1 1 1 524 200 300 02 300 11 300 41 300 42 301 01 CASSY Lab Stand base, V-shape, 20 cm Saddle base Stand rod, 25 cm Stand rod, 47 cm Leybold multiclamp additionally recommended: 1 PC with Windows 95/NT or higher 1 1 2 1 1 2 1 1 ß 2 · Dp · A2 2 r · (A2 – A2 ) 2 1 Note: In the first three experiments, the precision manometer is used to measure pressures. In addition to a pressure scale, it is provided with a further scale which indicates the flow speed directly when measuring with the pressure head sensor. In the last three experiments the pressure is measured with a pressure sensor and recorded and evaluated using the computer-assisted measuring system CASSY. The third experiment aims to determine flow speeds. Here, dynamic pressure (also called the “pressure head”) is measured using the pressure head sensor after Prandtl as the difference between the total pressure and the static pressure, and this value is used to calculate the speed at a known density U. 64 P 1.8.5.6 1 1 2 1 Mechanics Aerodynamics and hydrodynamics P 1.8.6 Measuring air resistance Drag coefficient cW: relationship between air resistance and body shape measuring the pressure with the precision manometer (P 1.8.6.2) P 1.8.6.1 Air resistance as a function of wind speed – measuring pressure with the precision manometer P 1.8.6.2 Drag coefficient cW: relationship between air resistance and body shape – measuring the pressure with the precision manometer P 1.8.6.3 Pressure curve on an airfoil profile – measuring the pressure with the precision manometer P 1.8.6.4 Air resistance as a function of wind speed – measuring the pressure with the pressure sensor and CASSY P 1.8.6.5 Drag coefficient cW: relationship between air resistance and body shape – measuring the pressure with the pressure sensor and CASSY P 1.8.6.6 Pressure curve on an airfoil profile – measuring the pressure with the pressure sensor and CASSY A flow of air exercises a force FW on a body in the flow which is parallel to the direction of the flow; this force is called the air resistance. This force depends on the flow speed v, the crosssection A of the body perpendicular to the flow direction and the shape of the body. The influence of the body shape is described using the so-called drag coefficient cw, whereby the air resistance is determined as: U Fw = cw · · v2 · A 2 The first experiment examines the relationship between the air resistance and the flow speed using a circular disk, while the second experiment determines the drag coefficient cw for various flow bodies with equal cross-sections. In both cases, the flow speed is measured using a pressure head sensor and the air resistance with a dynamometer. The aim of the third experiment is to measure the static pressure p at various points on the underside of an airfoil profile. The measured curve not only illustrates the air resistance, but also explains the lift acting on the airfoil. Note: In the first three experiments, the precision manometer is used to measure pressures. In addition to a pressure scale, it is provided with a further scale which indicates the flow speed directly when measuring with the pressure head sensor. In the last three experiments the pressure is measured with a pressure sensor and recorded and evaluated using the computer-assisted measuring system CASSY. P 1.8.6.4 – 5 1 1 1 1 1 1 1 1 1 1 2 1 1 P 1.8.6.1– 2 P 1.8.6.3 Cat. No. 373 04 373 06 373 071 373 075 373 14 373 13 373 10 373 70 524 010 524 066 Description Suction and pressure fan Open aerodynamics working section Aerodynamics accessories 1 Measurement trolley for wind tunnel Sector dynamometer Pressure head Precision manometer Air foil model Sensor CASSY Pressure sensor S, ± 70 hPa 1 1 1 1 1 1 1 1 1 1 1 1 1 1 524 200 300 02 300 11 300 42 301 01 CASSY Lab Stand base, V-shape, 20 cm Saddle base Stand rod, 47 cm Leybold multiclamp additionally recommended: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 2 P 1.8.6.6 1 1 1 1 1 1 1 65 Aerodynamics and hydrodynamics P 1.8.7 Measurements in a wind tunnel P 1.8.7.1 P 1.8.7.2 Recording the airfoil profile polars in a wind tunnel Measuring students’ own airfoils and panels in the wind tunnel Verifying the Bernoulli equation – measuring with the precision manometer Verifying the Bernoulli equation – measuring with the pressure sensor and CASSY Mechanics P 1.8.7.3 P 1.8.7.4 Recording the airfoil profile polars in a wind tunnel (P 1.8.7.1) The wind tunnel provides a measuring configuration for quantitative experiments on aerodynamics that ensures an airflow which has a constant speed distribution with respect to both time and space. Among other applications, it is ideal for measurements on the physics of flight. In the first experiment, the air resistance fW and the lift FA of an airfoil are measured as a function of the angle of attack a of the airfoil against the direction of flow. In a polar diagram, FW is graphed as a function of FA with the angle of attack a as the parameter. From this polar diagram, we can read e. g. the optimum angle of attack. In the second experiment, the students perform comparable measurements on airfoils of their own design. The aim is to determine what form an airfoil must have to obtain the smallest possible quotient FW /FA at a given angle of attack a. The last two experiments verify the Bernoulli equation. The difference between the total pressure and the static pressure is measured as a function of the cross-section, whereby the cross-section of the wind tunnel is gradually reduced by means of a builtin ramp. If we assume that the continuity equation applies, the cross-section A provides a measure of the flow speed v due to v · A0 v= 0 A v0: flow speed at cross-section A0 The experiment verifies the following relationship, which follows from the Bernoulli equation: 1 Dp “ 2 A P 1.8.7.1-2 P 1.8.7.3 1 1 1 1 1 1 Cat. No. 373 12 373 04 373 075 373 08 373 14 373 13 373 10 524 010 524 066 Description Wind tunnel Suction and pressure fan Measurement trolley for wind tunnel Aerodynamics accessories 2 Sector dynamometer Pressure head Precision manometer Sensor CASSY Pressure sensor S, ± 70 hPa 1 1 1 1 1 524 200 301 01 300 11 CASSY Lab Leybold multiclamp Saddle base additionally required: PC with Windows 95/NT or higher 66 P 1.8.7.4 1 1 1 1 1 1 1 1 1 Heat Table of contents Heat P2 Heat P 2.1 P 2.1.1 P 2.1.2 P 2.1.3 Thermal expansion Thermal expansion of solid bodies Thermal expansion of liquids Thermal anomaly of water 69 70 71 P 2.5 P 2.5.1 P 2.5.2 P 2.5.3 Kinetic theory of gases Brownian motion of molecules Laws of gases Specific heat of gases 81 82 83 P 2.2 P 2.2.1 P 2.2.2 Heat transfer Thermal conduction Solar collector 72 73 P 2.6 P 2.6.1 P 2.6.2 Thermodynamic cycle Hot-air motor: qualitative experiments Hot-air motor: quantitative experiments Heat pump 84–85 86–87 88 P 2.3 P 2.3.1 P 2.3.2 P 2.3.3 P 2.3.4 Heat as a form of energy Mixing temperatures Heat capacities Conversion of mechanical energy into heat energy Conversion of electrical energy into heat energy 74 75 76 77 P 2.6.3 P 2.4 P 2.4.1 P 2.4.2 P 2.4.3 Phase transitions Melting heat and evaporation heat Measuring vapor pressure Critical temperature 78 79 80 68 Heat Thermal expansion P 2.1.1 Thermal expansion of solid bodies P 2.1.1.1 Thermal expansion of solid bodies – measuring using STM equipment Thermal expansion of solid bodies – measuring using the expansion apparatus Measuring the longitudinal expansion of solid bodies as a function of temperature P 2.1.1.2 P 2.1.1.3 Measuring the longitudinal expansion of solid bodies as a function of temperature (P 2.1.1.3) Cat. No. 381 331 381 332 381 333 340 82 314 04 301 21 301 27 301 26 301 25 301 09 666 555 664 248 Description Pointer for linear expansion Al-tube, l = 22 cm, d = 8 mm Fe-tube, l = 44 cm, d = 8 mm Dual scale Support clip, for plugging in Stand base MF Stand rod, 50 cm, 10 mm dia. Stand rod, 25 cm, 10 mm dia. Clamping block MF Bosshead S Universal Bunsen clamp S Erlenmeyer flask, 50 ml 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 200 69304 Rubber stopper with hole 665 226 667 194 664 183 311 78 303 22 381 341 361 15 381 36 382 34 303 28 664 185 666 768 Connector, straight, 6 .... 8 mm dia. Tubing, silicone, int. dia. 7 mm/1.5 mm, 1 m Petri dish, 100 x 20 mm Tape measure, 1.5 m /1 mm Alcohol burner, metal Expansion apparatus Dial gauge Holder for dial gauge Thermometer, -10 to +110 °C Steam generator, 550 W/230 V Petri dish, 150 x 25 mm Circulation thermostat 30 ... 100 °C The relationship between the length s and the temperature P of a liquid is approximately linear: s = s0 · (1 + a · P) s0: length at 0°C, P: temperature in °C The linear expansion coefficient a is determined by the material of the solid body. We can conduct measurements on this topic using e.g. thin tubes through which hot water or steam flows. In the first experiment, steam is channeled through different tube samples. The thermal expansion is measured in a simple arrangement, and the dependency on the material is demonstrated. The second experiment measures the increase in length of various tube samples between room temperature and steam temperature using the expansion apparatus. The effective length s0 of each tube can be defined as 200, 400 or 600 mm. In the final experiment, a circulation thermostat is used to heat the water, which flows through various tube samples. The expansion apparatus measures the change in the lengths of the tubes as a function of the temperature P (cf. diagram). P 2.1.1.2 P 2.1.1.1 P 2.1.1.3 Thermal expansion of solid bodies – measuring using the expansion apparatus (P 2.1.1.2) 69 Thermal expansion P 2.1.2 Thermal expansion of liquids P 2.1.2.1 Determining the volumetric expansion coefficient of liquids Heat Determining the volumetric expansion coefficient of liquids (P 2.1.2.1 b) Cat. No. Description V = V0 · (1 + g · P) V0: volume at 0°C, P: temperature in °C When determining the volumetric expansion coefficient g, it must be remembered that the vessel in which the liquid is heated also expands. In this experiment, the volumetric expansion coefficients of water and methanol are determined using a volume dilatometer made of glass. An attached riser tube with a known cross-section is used to measure the change in volume. i. e. the change in volume is determined from the rise height of the liquid. 382 15 382 34 666 193 666 190 315 05 666 767 664 104 300 02 300 42 301 01 666 555 671 9720 Dilatometer, 50 ml Thermometer, -10° to + 110 °C Temperature sensor NiCr-Ni Digital thermometer with 1 input School and laboratory balance 311, 311 g Hot plate, 150 mm dia., 1500 W Beaker, 400 ml, ss., hard glass Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Universal clamp, 0...80 mm dia. Ethanol, fully denaturated, 1 l P 2.1.2.1 (a) 1 1 1 1 1 1 1 2 2 1 70 P 2.1.2.1 (b) 1 1 1 1 1 1 1 1 2 2 1 In general, liquids expands more than solids when heated. The relationship between the Volume V and the temperature P of a liquid is approximately linear here: Heat Thermal expansion P 2.1.3 Thermal anomaly of water P 2.1.3.1 Investigating the density maximum of water Investigating the density maximum of water (P 2.1.3.1 b) Cat. No. Description 667 505 382 36 666 190 666 193 666 845 664 195 665 008 307 66 300 02 300 42 301 01 301 10 666 555 Device for demonstrating the anomaly of water Thermometer, -10° to + 40 °C Digital thermometer with 1 input Temperature sensor NiCr-Ni Magnetic stirrer, 0...2000 rpm Glass tank, 300 x 200 x 150 mm Funnel, 50 mm dia., plastic Rubber tubing, i. d. 8 mm Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Clamp with ring Universal Bunsen clamp S 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 When heated from a starting temperature of 0 °C, water demonstrates a critical anomaly: it has a negative volumetric expansion coefficient up to 4 °C, i.e. it contracts when heated. After reaching zero at 4 °C, the volumetric expansion coefficient takes on a positive value. As the density corresponds to the reciprocal of the volume of a quantity of matter, water has a density maximum at 4 °C. This experiment verifies the density maximum of water by measuring the expansion in a vessel with riser tube. Starting at room temperature, the complete setup is cooled in a constantly stirred water bath to about 1 °C, or alternatively allowed to gradually reach the ambient temperature after cooling in an ice chest or refrigerator. The rise height h is measured as a function of the temperature P. As the change in volume is very slight in relation to the total volume V0, we obtain the density A r(P) = r(0 °C) · 1 – · h(P) V0 P 2.1.3.1 (b) P 2.1.3.1 (a) ( ) A: cross-section of riser tube 71 Heat transfer P 2.2.1 Thermal conduction Heat P 2.2.1.1 Determining the heat conductivity of building materials using the single-plate method P 2.2.1.2 Determining the heat conductivity of building materials with the aid of a reference material of known thermal conductivity P 2.2.1.3 Damping of temperature variations using multi-layer walls Determining the heat conductivity of building materials with the aid of a reference material of known thermal conductivity (P 2.2.1.2) In the equilibrium state, the heat flow through a plate with the cross-section area A and the thickness d depends on the temperature difference P2 – P1 between the front and rear sides and on the thermal conductivity l of the plate material: DQ P – P1 =l·A· 2 Dt d The object of the first two experiments is to determine the thermal conductivity of building materials. In these experiments, sheets of building materials are placed in the heating chamber and their front surfaces are heated. The temperatures P1 and P2 are measured using measuring sensors. The heat flow is determined either from the electrical power of the hot plate or by measuring the temperature using a reference material with known thermal conductivity l0 which is pressed against the sheet of the respective building material from behind. P 2.2.1.2 1 1 1 1 3 2 Cat. No. 389 29 389 30 521 25 666 198 666 190 666 209 666 193 531 100 531 100 313 17 450 64 450 63 300 11 501 33 501 46 Description Calorimetric chamber Set of building materials for calorimetric chamber Transformer 2....12 V Digital temperature controller and indicator Digital thermometer with 1 input Digital thermometer with 4 inputs Temperature sensor NiCr-Ni Ammeter, AC, I < 2 A, e.g. Multimeter METRAmax 2 Voltmeter, AC, U < 12 V, e.g. Multimeter METRAmax 2 Stopclock II, 60 s/30 min Halogen lamp housing, 12 V, 50/100 W Halogen lamp, 12 V/100 W Saddle base Connecting lead, 100 cm, black, Ø 2,5 mm2 Pair of cables, 100 cm, red and blue * alternatively: digital thermometer with 4 inputs (666 209) 1 1 1 1 1* 2 1 1 1 3 1 The final experiment demonstrates the damping of temperature variations by means of two-layer walls. The temperature changes between day and night are simulated by repeatedly switching a lamp directed at the outside surface of the wall on and off. This produces a temperature “wave” which penetrates the wall; the wall in turn damps the amplitude of this wave. This experiment measures the temperatures PA on the outer surface, PZ between the two layers and PI on the inside as a function of time. Temperature variations in multi-layer walls (P 2.2.1.3) 72 P 2.2.1.3 1 1 1 1 3 1 1 1 1 2 P 2.2.1.1 Heat Heat transfer P 2.2.2 Solar collector P 2.2.2.1 Determining the efficiency of a solar collector as a function of the throughput volume of water P 2.2.2.2 Determining the efficiency of a solar collector as a function of the thermal insulation Determining the efficiency of a solar collector as a function of the throughput volume of water (P 2.2.2.1) Cat. No. Description 389 50 579 22 450 70 521 35 666 209 666 193 311 77 313 17 300 02 300 41 300 42 300 43 301 01 666 555 590 06 307 70 501 46 Solar collector STE miniature pump Flood light lamp, 1000 W Variable extra-low voltage transformer S Digital thermometer with 4 inputs Temperature sensor NiCr-Ni Steel tape measure, 2 m Stopclock II, 60 s/30 min Stand base, V-shape, 20 cm Stand rod, 25 cm Stand rod, 47 cm Stand rod, 75 cm Leybold multiclamp Universal clamp, 0...80 mm dia. Plastic beaker, 1000 ml Plastic tubing, PVC, i. d. 8 mm Pair of cables, 100 cm, red and blue 1 1 1 1 1 2 1 1 2 1 1 1 3 1 1 1 1 A solar collector absorbs radiant energy to heat the water flowing through it. When the collector is warmer than its surroundings, it loses heat to its surroundings through radiation, convection and heat conductivity. These losses reduce the efficiency DQ J= DE i. e. the ratio of the emitted heat quantity DQ to the absorbed radiant energy DE. In both experiments, the heat quantity DQ emitted per unit of time is determined from the increase in the temperature of the water flowing through the apparatus, and the radiant energy absorbed per unit of time is estimated on the basis of the power of the lamp and its distance from the absorber. The throughput volume of the water and the heat insulation of the solar collector are varied in the course of the experiment. P 2.2.2.1-2 73 Heat quantity P 2.3.1 Mixing temperatures Heat P 2.3.1.1 Measuring the temperature of a mixture of hot and cold water Measuring the temperature of a mixture of hot and cold water (P 2.3.1.1 a) When cold water with the temperature P1 is mixed with warm or hot water having the temperature P2, an exchange of heat takes place until all the water reaches the same temperature. If no heat is lost to the surroundings, we can formulate the following for the mixing temperature: m1 m2 Pm = P + P m1 + m2 1 m1 + m2 2 m1, m2: mass of cold and warm water respectively Thus the mixing temperature Pm is equivalent to a weighted mean value of the two temperatures P1 and P2. The use of the Dewar flask in this experiment essentially prevents the loss of heat to the surroundings. This vessel has a double wall; the intermediate space is evacuated and the interior surface is mirrored. The water is stirred thoroughly to ensure a complete exchange of heat. This experiment measures the mixing temperature Pm for different values for P1, P2, m1, and m2. Cat. No. Description 386 48 384 161 382 34 666 193 666 190 315 23 313 07 666 767 664 104 Dewar vessel Lid for Dewar vessel Thermometer, -10° to + 110 °C Temperature sensor NiCr-Ni Digital thermometer with 1 input School and laboratory balance 610 tare, 610 g Stopclock I, 30 s/15 min Hot plate, 150 mm dia., 1500 W Beaker, 400 ml, ss, hard glass P 2.3.1.1 (a) 1 1 1 1 1 1 2 74 P 2.3.1.1 (b) 1 1 1 1 1 1 1 2 Heat Heat quantity P 2.3.2 Heat capacities P 2.3.2.1 Determining the specific heat capacity of solids Determining the specific heat capacity of solids (P 2.3.2.1 a) Cat. No. Description 386 48 384 161 384 34 384 35 384 36 315 76 303 28 382 34 666 190 666 193 315 23 300 02 300 42 301 01 666 555 667 614 664 104 667 194 Dewar vessel Lid for Dewar vessel Heating apparatus Copper shot, 200 g Glass shot, 100 g Lead shot, 200 g Steam generator, 550 W/230 V Thermometer, -10° to + 110 °C Digital thermometer with 1 input Temperature sensor NiCr-Ni School and laboratory balance 610 tare, 610 g Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Universal Bunsen clamp S Heat-protective gloves, pair; length: 290 mm Beaker, 400 ml, ss, hard glass Silicone tubing, i. d. 7 x 1.5 mm, 1 m 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 When a body is heated or cooled, the absorbed heat capacity DQ is proportional to the change in temperature DP and to the mass m of the body: DQ = c · m · DP The proportionality factor c, the specific heat capacity of the body, is a quantity which depends on the respective material. To determine the specific heat capacity, various materials in particle form are weighed, heated in steam to the temperature P1 and poured into a weighed-out quantity of water with the temperature P2. After careful stirring, heat exchange ensures that the particles and the water have the same temperature Pm. The heat quantity released by the particles: DQ1 = c1 · m1 · (P1 · Pm) m1: mass of particles c1: specific heat capacity of particles is equal to the heat quantity absorbed by the water DQ2 = c2 · m2 · (Pm · P2) m2: mass of water The specific heat capacity of water c2 is assumed as a given. The temperature P1 corresponds to the temperature of the steam. Therefore, the specific heat quantity c1 can be calculated from the measurement quantities P2, Pm, m1 and m2 . P 2.3.2.1 (a) P 2.3.2.1 (b) 75 Heat quantity P 2.3.3 Conversion of mechanical energy P 2.3.3.1 Converting mechanical energy into heat energy – recording and evaluating measured values manually P 2.3.3.2 Converting mechanical energy into heat energy – recording and evaluating measured values with CASSY Heat Converting mechanical energy into heat energy – recording and evaluating measured values manually (P 2.3.3.1) Energy is a fundamental quantity of physics. This is because the various forms of energy can be converted from one to another and are thus equivalent to each other, and because the total energy is conserved in the case of conversion in a closed system. These two experiments show the equivalence of mechanical and heat energy. A hand crank is used to turn various calorimeter vessels on their own axes, and friction on a nylon belt causes them to become warmer. The friction force is equivalent to the weight G of a suspended weight. For n turns of the calorimeter, the mechanical work is thus Wn = G · n · S · d d: diameter of calorimeter This results in an increase in the temperature of the calorimeter which corresponds to the specific heat capacity Qn = m · c · (Pn – P0), c: specific heat capacity, m: weight, Pn: temperature after n turns To confirm the relationship Qn = Wn the two quantities are plotted together in a diagram. In the first experiment, the measurement is conducted and evaluated manually point by point. The second experiment takes advantage of the computer-assisted measuring system CASSY. P 2.3.3.1 (b) 1 1 1 1 1 1 1 1 1 1 1 P 2.3.3.1 (a) Cat. No. Description 388 00 388 01 388 02 388 03 388 04 388 05 388 24 666 190 666 193 524 010 337 46 524 045 524 034 501 16 524 200 300 02 300 40 300 41 301 07 301 11 Equivalent of heat, basic apparatus Water calorimeter Copper-block calorimeter with heating coil Aluminum-block calorimeter with heating Large aluminum-block calorimeter with heating coil Thermometer for calorimeters Weight with hook, 5 kg Digital thermometer with 1 input Temperature sensor NiCr-Ni Sensor CASSY Forked light barrier, infra-red Temperature box (NiCrNi/NTC) Timer box Multicore cable, 6-pole, 1.5 m long CASSY Lab Stand base, V-shape, 20 cm Stand rod, 10 cm Stand rod, 25 cm Simple bench clamp Clamp with jaw clamp additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 1 76 P 2.3.3.2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Heat Heat quantity P 2.3.4 Conversion of electrical energy P 2.3.4.1 Converting electrical into heat energy – measuring with the voltmeter and ammeter P 2.3.4.2 Converting electrical into heat energy – measuring with the joule and wattmeter Converting electrical into heat energy - measuring with the joule and wattmeter (P 2.3.4.2) Cat. No. Description 384 20 386 48 388 02 388 03 388 04 388 06 521 35 382 34 388 05 666 190 666 193 531 100 531 712 313 07 664 103 665 755 501 28 501 45 531 83 Electric calorimeter attachment Dewar vessel calorimeter with base Copper-block calorimeter with heating coil Aluminum-block calorimeter with heating Large aluminum-block calorimeter with heating coil Pair of connecting cables Voltage source, 0 … 12 V, e. g. Variable extra-low voltage transformer S Thermometer, -10° to + 110 °C Thermometer for calorimeters Digital thermometer with 1 input Temperature sensor NiCr-Ni Voltmeter, AC, U < 12 V, e.g. Multimeter METRAmax 2 Ammeter, I < 6 A, e.g. Multimeter METRAmax 3 Stopclock I, 30s/15min Beaker, 250 ml, ss, hard glass Graduated cylinder, 250 ml: 2 Connecting lead, Ø 2.5 mm2, 50 cm, black Pair of cables, 50 cm, red and blue Joule and wattmeter 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 Just like mechanical energy, electrical energy can also be converted into heat. We can use e.g. a calorimeter vessel with a wire winding to which a voltage is connected to demonstrate this fact. When a current flows through the wire, Joule heat is generated and heats the calorimeter. The supplied electrical energy W(t) = U · l · t is determined in the first experiment by measuring the voltage U, the current I and the time t, and in the second experiment measured directly using the joule and wattmeter. This results in a change in the temperature of the calorimeter which corresponds to the specific heat capacity Q(t) = m · c · (P(t) – P(0)), c: specific heat capacity, m: mass, P(t): temperature at time t To confirm the equivalence Q(t) = W(t) the two quantities are plotted together in a diagram. P 2.3.4.2 (b) P 2.3.4.2 (a) P 2.3.4.1 (b) P 2.3.4.1 (a) 77 Phase transitions P 2.4.1 Melting heat and evaporation heat P 2.4.1.1 Determining the specific evaporation heat of water P 2.4.1.2 Determining the specific melting heat of ice Heat Determining the specific evaporation heat of water (P 2.4.1.1) When a substance is heated at a constant pressure, its temperature generally increases. When that substance undergoes a phase transition, however, the temperature does not increase even when more heat is added, as the heat is required for the phase transition. As soon as the phase transition is complete, the temperature once more increases with the additional heat supplied. Thus, for example, the specific evaporation heat QV per unit of mass is required for evaporating water, and the specific melting heat QS per unit of mass is required for melting ice. To determine the specific evaporation heat Qv of water, pure steam is fed into the calorimeter in the first experiment, in which cold water is heated to the mixing temperature Pm. The steam condenses to water and gives off heat in the process; the condensed water is cooled to the mixing temperature. The experiment measures the starting temperature P2 and the mass m2 of the cold water, the mixing temperature Pm and the total mass m = m1 + m2 By comparing the amount of heat given off and absorbed, we can derive the equation m · c · (Pm – P1) + m2 · c · (Pm – P2) QV = 1 . m1 P1 ≈ 100 hC, c: specific heat capacity of water In the second experiment, pure ice is filled in a calorimeter, where it cools water to the mixing temperature Pm, in order to determine the specific melting heat. The ice absorbs the melting heat and melts into water, which warms to the mixing temperature. Analogously to the first experiment, we can say for the specific melting heat: m · c · (Pm – P1) + m2 · c · (Pm – P2) QS = 1 . m1 P1 = 0 hC Cat. No. Description 386 48 Dewar vessel 1 1 P 2.4.1.2 (a) 1 1 1 1 1 1 P 2.4.1.1 (b) P 2.4.1.1 (a) 384 17 303 28 303 25 382 34 666 190 666 193 315 23 300 02 300 42 301 01 666 555 664 104 667 194 590 06 Water separator Steam generator, 550 W/230 V Immersion heater Thermometer, -10° to + 110 °C Digital thermometer with 1 input Temperature sensor NiCr-Ni School and laboratory balance 610 Tara, 610 g Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Universal Bunsen clamp S Beaker, 400 ml, ss, hard glass Silicone tubing, int. dia. 7 x 1.5 mm, 1 m Plastic beaker, 1000 ml 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 1 1 78 P 2.4.1.2 (b) 1 1 1 1 1 1 Heat Phase transitions P 2.4.2 Measuring vapor pressure P 2.4.2.1 Recording the vapor pressure curve of water up to 1 bar P 2.4.2.2 Recording the vapor pressure curve of water up to 50 bar Recording the vapor pressure curve of water up to 50 bar (P 2.4.2.2) Cat. No. 664 315 665 305 667 186 665 255 378 031 378 045 378 050 378 701 524 010 524 200 309 00 335 501 11 Description Double-necked round-bottom flask, 250 ml, ST 19/26, GL 18 Core/threads ST 19/26, with GL 18 Vacuum rubber tubing, int. dia. 8 x 5 mm, 1 m Stopcock, 3-way valve, with ST stopcock, 8 mm dia., T-shape Small flange DN 16 KF with hose nozzle Centering ring DN 16 KF Clamping ring DN 10/16 KF High-vacuum grease Sensor CASSY CASSY Lab Rod 10 x 225 mm with thread M6 Extension cable, 15-pole 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The vapor pressure p of a liquid-vapor mixture in a closed system depends on the temperature T. Above the critical temperature, the vapor pressure is undefined. The substance is gaseous and cannot be liquefied no matter how high the pressure. The increase in the vapor-pressure curve p(T) is determined by several factors, including the molar evaporation heat qv of the substance: qv dp T· = (Clausius-Clapeyron) dT v1 – v2 T: absolute temperature v1: molar volume of vapor v2: molar volume of liquid As we can generally ignore v2 and qv hardly varies with T, we can derive a good approximation from the law of ideal gases: qv ln p = ln p0 – R·T In the first experiment, the vapor pressure curve of water below the normal boiling point is recorded with the computer-assisted measuring system CASSY. The water is placed in a glass vessel, which was sealed beforehand while the water was boiling at standard pressure. The vapor pressure p is measured as a function of the temperature T when cooling and subsequently heating the system, respectively. The high-pressure steam apparatus is used in the second experiment for measuring pressures of up to 50 bar. The vapor pressure can be read directly from the manometer of this device. A thermometer supplies the corresponding temperature. The measured values are recorded and evaluated manually point by point. 524 045 524 065 Temperature-box (NiCrNi/NTC) Absolute pressure sensor S, 0...1500 hPa 666 216 300 02 300 43 666 555 301 01 302 68 666 685 666 711 666 712 667 614 385 16 664 109 NiCr-Ni-temperature sensor Stand base, V-shape, 20 cm Stand rod, 75 cm Universal clamp, 0 ... 80 mm dia. Leybold multiclamp Ring with stem Wire gauze, 160 x 160 mm Butane gas burner, gas and air regulation Butane cartridges 200g, set of 3 Heat protective gloves, pair High-pressure steam boiler Beaker, 25 ml, ss, hard glass Stand base, V-shape, 28 cm Stand rod, 25 cm Safety goggles for wearing over glasses additionally recommended: PC with Windows 95/NT or higher 3 1 1 1 1 1 300 01 300 41 667 613 1 P 2.4.2.2 1 1 1 1 1 1 1 1 1 1 1 P 2.4.2.1 79 Phase transitions P 2.4.3 Critical temperature Heat P 2.4.3.1 Investigating a liquid-vapor mixture at the critical point Investigating a liquid-vapor mixture at the critical point (P 2.4.3.1 b) The critical point of a real gas is defined by the critical pressure pc, the critical density Uc and the critical temperature Tc. Below the critical temperature, the substance is gaseous for a sufficiently great molar volume – it is termed a vapor – and is liquid at a sufficiently small molar volume. Between these extremes, a liquid-vapor mix exists, in which the vapor component increases with the molar volume. As liquid and vapor have different densities, they are separated in a gravitational field. As the temperature rises, the density of the liquid decreases and that of the vapor increases, until finally at the critical temperature both densities have the value of the critical density. Liquid and vapor mix completely, and the phase boundary disappears. Above the critical temperature, the substance is gaseous, regardless of the molar volume. This experiment investigates the behavior of sulfur hexafluoride (SF6) close to the critical temperature. The critical temperature of this substance is Tc = 318.7 K and the critical pressure is pc = 37.6 bar. The substance is enclosed in a pressure chamber designed so that hot water or steam can flow through the mantle. The dissolution of the phase boundary between liquid and gas while heating the substance, and its restoration during cooling, are observed in projection on the wall. As the system approaches the critical point, the substance scatters short-wave light particularly intensively; the entire contents of the pressure chamber appears red-brown. This critical opalescence is due to the variations in density, which increase significantly as the system approaches the critical point. Note: The dissolution of the phase boundary during heating can be observed best when the pressure chamber is heated as slowly as possible using a circulation thermostat. Cat. No. Description 371 401 450 60 450 51 460 20 460 03 461 11 Pressure chamber for demonstrating the critical temperature Lamp housing Lamp, 6 V/30 W Aspherical condensor Lens, f = + 100 mm Right angled prism Transformer, 6 V AC, 12 V AC/ 30 W Thermometer, -10 to +150 °C Temperatur sensor, NiCr.Ni Digital thermometer with one input Steam generator, 550 W/230 V Silicone tubing. int. dia. 7 x 1.5 mm, 1 m Beaker, 400 ml, ss, hard glass Circulation thermostat, + 30 - 100 °C Small optical bench Stand base, V-shape, 28 cm Leybold multiclamp 1 1 1 1 1 1 1 1 521 210 382 33 666 193 666 190 303 28 667 194 664 104 666 768 460 43 300 01 301 01 1 2 1 1 1 1 4 1 1 4 2 80 P 2.4.3.1(b) 1 1 1 1 1 1 1 1 1 P 2.4.3.1(a) Heat Kinetic theory of gases P 2.5.1 Brownian motion of molecules P 2.5.1.1 Brownian motion of smoke particles Brownian motion of smoke particles (P 2.5.1.1) Cat. No. 662 078 372 51 450 60 450 51 460 20 521 210 Description Microscope MIC 805 Smoke chamber Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC/ 30 W Stand base, V-shape, 20 cm 1 1 1 1 1 1 1 A particle which is suspended in a gas constantly executes a motion which changes in its speed and in all directions. J. Perrin first explained this molecular motion, discovered by R. Brown, which is caused by bombardment of the particles with the gas molecules. The smaller the particle is, the more noticeably it moves. The motion consists of a translational component and a rotation, which also constantly changes. In this experiment, the motion of smoke particles in the air is observed using a microscope. 300 02 Schematic diagram of Brownian motion of molecules P 2.5.1.1 81 Kinetic theory of gases P 2.5.2 Laws of gases Heat P 2.5.2.1 Pressure-dependency of the volume of a gas at a constant temperature (Boyle-Mariotte’s law) P 2.5.2.2 Temperature-dependency of the volume of a gas at a constant pressure (Gay-Lussac’s law) P 2.5.2.3 Temperature-dependency of the pressure of a gas at a constant volume (Amontons’ law) Pressure-dependency of the volume of a gas at a constant temperature (Boyle-Mariotte’s law) (P 2.5.2.1) The gas thermometer consists of a glass tube closed at the bottom end, in which a mercury stopper seals the captured air at the top. The volume of the air column is determined from its height and the cross-section of the glass tube. When the pressure at the open end is altered using a hand pump, this changes the pressure on the sealed side correspondingly. The temperature of the entire gas thermometer can be varied using a water bath. In the first experiment, the air column is maintained at a constant room temperature T. At an external pressure p0, it has a volume of V0 bounded by the mercury stopper. The pressure p in the air column is reduced by evacuating air at the open end, and the increased volume V of the air column is determined for different pressure values p. The evaluation confirms the relationship p · V = p0 · V0 for T = const. (Boyle-Mariotte’s law) In the second experiment, the gas thermometer is placed in a water bath of a specific temperature which is allowed to gradually cool. The open end is subject to the ambient air pressure, so that the pressure in the air column is constant. This experiment measures the volume V of the air column as a function of the temperature T of the water bath. The evaluation confirms the relationship V “ T for p = const. (Gay-Lussac’s law) In the final experiment, the pressure p in the air column is constantly reduced by evacuating the air at the open end so that the volume V of the air column also remains constant as the temperature drops. This experiment measures the pressure p of the air column as a function of the temperature T of the water bath. The evaluation confirms the relationship p “ T for V = const. (Amontons’ law) P 2.5.2.2 1 1 1 1 1 2 1 1 Cat. No. 382 00 666 190 666 193 300 02 300 42 301 11 375 58 666 767 664 103 Description Gas thermometer Digital thermometer with one input Temperatur sensor, NiCr.Ni Stand base, V-shape, 20 cm Stand rod, 47 cm Clamp with jaw clamp Hand vacuum and pressure pump Hot plate, 150 mm dia., 1500 W Beaker, 400 ml, ss, hard glass 1 1 1 2 1 Pressure-dependency of the volume at a constant temperature (P 2.5.2.1) 82 P 2.5.2.3 1 1 1 1 1 2 1 1 1 P 2.5.2.1 Heat Kinetic theory of gases P 2.5.3 Spezific heat of gases P 2.5.3.1 Determining the adiabatic exponent Cp/CV of air after Rüchard P 2.5.3.2 Determining the adiabatic exponent Cp/CV of various gases using the gas elastic resonance apparatus Determining the adiabatic exponent Cp/CV of air after Rüchard (P 2.5.3.1) Determining the adiabatic exponent Cp/CV of various gases using the gas elastic resonance apparatus (P 2.5.3.2) Cat. No. 371 04 371 05 313 07 317 19 590 06 675 3100 371 07 665 914 665 918 522 621 Description Marriot’s flask, 10 l Oscillation tube, apparatus for determination of cp/cV Stopclock I, 30s/15min Aneroid barometer, 980 – 1045 mbar Plastic beaker, 1000 ml Vaseline, 50 g Gas elastic resonance apparatus Gas syringe with 3-way stopcock, 100 ml:1 Holder for gas syringe, 100 ml, plastic Function generator S 12, 0.1 Hz to 20 kHz 1 1 1 1 1 1 1 1 1 1 In the case of adiabatic changes in state, the pressure p and the volume V of a gas demonstrate the relationship p · V K = const. whereby the adiabatic exponent is defined as C k = p CV i.e. the ratio of the specific heat capacities Cp and CV of the respective gas. The first experiment determines the adiabatic exponent of air from the oscillation period of a ball which caps and seals a gas volume in a glass tube, whereby the oscillation of the ball around the equilibrium position causes adiabatic changes in the state of the gas. In the equilibrium position, the force of gravity and the opposing force resulting from the pressure of the enclosed gas are equal. A deflection from the equilibrium position by Wx causes the pressure to change by A · Dx Dp = – k · p · , V A: cross-section of riser tube which returns the ball to the equilibrium position. The ball thus oscillates with the frequency f0 = 1 · 2S 575 451 Counter P Ammeter, AC, I = 1 A, e.g. Multimeter METRAmax 2 Stand base, V-shape, 20 cm Fine regulating valve for Minican gas cans Minican gas can, neon Minican gas can, carbon dioxide Three-way valve with ST-stopcock, 8 mm dia., T-shape Silikone tubing, i. d. 7 x 1.5 mm, 1 m Connecting lead, blue, 50 cm Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, red and blue 531 100 300 02 660 980 660 985 660 999 665 255 667 194 500 422 501 45 501 46 P 2.5.3.2 1 1 1 1 1 1 1 1 1 1 1 P 2.5.3.1 ö k · p · A2 , m·V around its equilibrium position. In the second experiment, the adiabatic exponent is determined using the gas elastic resonance apparatus. Here, the air column is sealed by a magnetic piston which is excited to forced oscillations by means of an alternating electromagnetic field. The aim of the experiment is to find the characteristic frequency f0 of the system, i.e. the frequency at which the piston oscillates with maximum amplitude. Other gases, such as carbon dioxide and nitrogen, can alternatively be used in this experiment. 83 Thermodynamic cycle P 2.6.1 Hot-air engine: qualitative experiments P 2.6.1.1 Operating a hot-air engine as a thermal engine Heat Operating a hot-air engine as a thermal engine (P 2.6.1.1) The hot-air engine (invented by R. Stirling, 1816) is the oldest thermal engine, along with the steam engine. In greatly simplified terms, its thermodynamic cycle consists of an isothermic compression at low temperature, an isochoric application of heat, an isothermic expansion at high temperature and an isochoric emission of heat. The displacement piston and the working piston are connected to a crankshaft via tie rods, whereby the displacement piston leads the working piston by 90°. When the working piston is at top dead center (a), the displacement piston is moving downwards, displacing the air into the electrically heated zone of the cylinder. Here, the air is heated, expands and forces the working piston downward (b). The mechanical work is transferred to the flywheel. When the working piston is at bottom dead center (c), the displacement piston is moving upwards, displacing the air into the water-cooled zone of the cylinder. The air cools and is compressed by the working cylinder (d). The flywheel delivers the mechanical work required to execute this process. Cat. No. 388 182 Description Hot-air engine 1 562 11 562 12 562 21 562 18 501 33 388 181 521 230 U-core with yoke Clamping device Mains coil with 500 turns for 230 V Extra-low-voltage coil, 50 turns Connecting lead, Ø 2.5 mm2, 100 cm, black Submersible pump, 12 V Low-voltage power supply Silicone tubing, int. dia. 7 x 1.5 mm, 1 m * additionally recommended 1 1 1 1 2 1* 1* 667 194 2* The experiment qualitatively investigates the operation of the hotair engine as a thermal engine. Mechanical power is derived from the engine by braking at the brake hub. The voltage of the heating filament is varied in order to demonstrate the relationship between the thermal power supplied and the mechanical power removed from the system. The no-load speed of the motor for each case is used as a measure of the mechanical power produced in the system. 84 P 2.6.1.1 Heat Thermodynamic cycle P 2.6.1 Hot-air engine: qualitative experiments P 2.6.1.3 Operating the hot-air engine as a heat pump and a refrigerating machine Operating the hot-air engine as a heat pump and a refrigerating machine (P 2.6.1.3) Cat. No. 388 182 388 19 347 35 347 36 Description Hot-air engine Thermometer Experiment motor Control unit for experiment motor 1 1 1 1 388 181 521 230 Immersion pump 12 V Low-voltage power supply Silicone tubing, int. dia. 7 x 1.5 mm, 1 m * additionally recommended 1* 1* 2* 667 194 Depending on the direction of rotation of the crankshaft, the hotair engine operates as either a heat pump or a refrigerating machine when its flywheel is externally driven. When the displacement piston is moving upwards while the working piston is at bottom dead center, it displaces the air in the top part of the cylinder. The air is then compressed by the working piston and transfers its heat to the cylinder head, i.e. the hot-air motor operates as a heat pump. When run in the opposite direction, the working piston causes the air to expand when it is in the top part of the cylinder, so that the air draws heat from the cylinder head; in this case the hot-air engine operates as a refrigerating machine. The experiment qualitatively investigates the operation of the hotair engine as a heat pump and a refrigerating machine. In order to demonstrate the relationship between the externally supplied mechanical power and the heating or refrigerating power, respectively, the speed of the electric motor is varied and the change in temperature observed. Experiments to the hot-air engine can also be realized with the hot-air engine P (388 176) P 2.6.1.3 85 Thermodynamic cycle P 2.6.2 Hot-air engine: quantitative experiments P 2.6.2.1 Frictional losses in the hot-air engine (calorific determination) P 2.6.2.2 Determining the efficiency of the hot-air engine as a heat engine P 2.6.2.3 Determining the efficiency of the hot-air engine as a refrigerating machine Heat Frictional losses in the hot-air engine (calorific determination) (P 2.7.2.1) When the hot-air engine is operated as a heat engine, each engine cycle withdraws the amount of heat Q1 from reservoir 1, generates the mechanical work W and transfers the difference Q2 = Q1 – W to reservoir 2. The hot-air engine can also be made to function as a refrigerating machine while operated in the same rotational direction by externally applying the mechanical work W. In both cases, the work WF converted into heat in each cycle through the friction of the piston in the cylinder must be taken into consideration. In order to determine the work of friction WF in the first experiment, the temperature increase DTF in the cooling water is measured while the hot-air engine is driven using an electric motor and the cylinder head is open. The second experiment determines the efficiency W J= W + Q2 of the hot-air engine as a heat engine. The mechanical work W exerted on the axle in each cycle can be calculated using the external torque N of a dynamometrical brake which brakes the hot-air engine to a speed f. The amount of heat Q2 given off corresponds to a temperature increase DT in the cooling water. The final experiment determines the efficiency Q1 J= Q1 – Q2 of the hot-air engine as a refrigerating machine. Here, the hot-air engine with closed cylinder head is driven using an electric motor and Q1 is determined as the electrical heating energy required to maintain the cylinder head at the ambient temperature. 388 181 521 230 P 2.6.2.2 1 1 1 1 1 1 1 1 1 1 1 1 Cat. No. 388 182 388 221 347 35 347 36 562 11 562 12 562 21 562 18 521 35 Description Hot-air engine Accessories for hot-air engine Experiment motor Control unit for experiment motor U-core with yoke Clamping device Mains coil with 500 turns for 230 V Extra-low voltage coil, 50 turns Variable extra-low voltage transformer S 1 1 1 1 575 471 Counter S 1 1 1 337 46 501 16 Forked light barrier, infra-red Multi-core cable, 6-pole, 1.5 m 531 100 531 712 313 17 Multimeter METRAmax 2 Multimeter METRAmax 3 Stopclock II, 60 s/30 min 1 314 141 382 36 Precision dynamometer, 1.0 N Thermometer, -10° to + 40 °C 1 1 1 1 300 02 300 41 300 42 300 51 301 01 590 06 342 61 Stand base, V-shape, 20 cm Stand rod, 25 cm Stand rod, 47 cm Stand rod, right-angled Leybold multiclamp Plastic beaker, 1000 ml Set of 12 weights, 50 g each Connecting lead, Ø 2.5 mm2, 100 cm, black Pair of cables, 50 cm, red and blue 1 1 2 1 1 1 2 1 1 1 3 1 Immersion pump 12 V Low voltage power supply Silicone tubing, int. dia. 7 x 1.5 mm, 1 m * additionally recommended 1* 1* 2* 1* 1* 2* 1* 1* 2* 501 33 501 45 667 194 86 P 2.6.2.3 1 1 1 1 1 1 1 1 1 1 1 P 2.6.2.1 1 1 1 3 1 Heat Thermodynamic cycle P 2.6.2 Hot-air engine: quantitative experiments P 2.6.2.4 Hot-air engine as a heat engine: recording and evaluating the pV diagram with CASSY Hot-air engine as a heat engine: recording and evaluating the pV diagram with CASSY (P 2.6.2.4) Cat. No. 388 182 562 11 562 12 562 21 562 18 529 031 524 031 524 064 Description Hot-air engine U-core with yoke Clamping device Mains coil with 500 turns for 230 V Extra-low voltage coil, 50 turns Displacement transducer Current supply box Pressure sensor S, ± 2000 hPa 1 1 1 1 1 1 1 1 524 010 524 200 309 48 352 08 501 46 501 33 388 181 521 230 Sensor CASSY CASSY Lab Cord, 10 m Helical spring, 5 N; 0.25 N/cm Pair of cables, 100 cm, red and blue Connecting lead, Ø 2.5 mm2, 100 cm, black Immersion pump 12 V Low-voltage power supply Silicone tubing, int. dia. 7 x 1.5 mm, 1 m additionally required: PC with Windows 95/NT or higher * additionally recommended 1 1 1 1 1 2 1* 1* Thermodynamic cycles are often described as a closed curve in a pV diagram (p: pressure, V: volume). The work added to or withdrawn from the system (depending on the direction of rotation) corresponds to the area enclosed by the curve. In this experiment, the pV diagram of the hot air engine as a heat engine is recorded using the computer-assisted measured value recording system CASSY. The pressure sensor measures the pressure p in the cylinder and a displacement sensor measures the position s, from which the volume is calculated, as a function of the time t. The measured values are displayed on the screen directly in a pV diagram. In the further evaluation, the mechanical work performed as piston friction per cycle W = – ∫ p · dV and from this the mechanical power P=W·f f: no-load speed are calculated and plotted in a graph as a function of the no-load speed. 667 194 P 2.6.2.4 2* 1 87 Thermodynamic cycle P 2.6.3 Heat pump Heat P 2.6.3.1 Determining the efficiency of the heat pump as a function of the temperature differential P 2.6.3.2 Investigating the function of the expansion valve of the heat pump P 2.6.3.3 Analyzing the thermodynamic cycle of the heat pump using the Mollier diagram Determining the efficiency of the heat pump as a function of the temperature differential (P 2.6.3.1) The heat pump extracts heat from a reservoir with the temperature T1 through vaporization of a coolant and transfers heat to a reservoir with the temperature T2 through condensation of the coolant. In the process, compression in the compressor (a-b) greatly heats the gaseous coolant. It condenses in the liquefier (c-d) and gives up the released condensation heat DQ2 to the reservoir T2. The liquefied coolant is filtered and fed to the expansion valve (e-f) free of bubbles. This regulates the supply of coolant to the vaporizer (g-h). In the vaporizer, the coolant once again becomes a gas, withdrawing the necessary evaporation heat DQ1 from the reservoir T1. P 2.6.3.2 1 1 2 1 1* 2* Cat. No. 389 521 531 83 666 209 666 193 502 05 313 12 575 713 Description Heat pump pT Joule and wattmeter Digital thermometer with four inputs Temperature sensor NiCr-Ni Measuring junction box Digital stopwatch Yt-recorder, 2 channels Safety connection lead, 50 cm, red Safety connection lead, 50 cm, blue Pair of cables, 50 cm, red and blue * additionally recommended 1 1 1 2 1 1 1* 2 2 2* 1 1 1 3 1 1 1* 2 2 2* 500 621 500 622 501 46 The aim of the first experiment is to determine the efficiency DQ2 e= DW of the heat pump as a function of the temperature differential DT = T2 – T1. The heat quantity DQ2 released is determined from the heating of water reservoir T2, while the applied electrical energy DW is measured using the joule and wattmeter. In the second experiment, the temperatures Tf and Th are recorded at the outputs of the expansion valve and the vaporizer. If the difference between these two temperatures falls below a specific limit value, the expansion valve chokes off the supply of coolant to the vaporizer. This ensures that the coolant in the vaporizer is always vaporized completely. In the final experiment, a Mollier diagram, in which the pressure p is graphed as a function of the specific enthalpy h of the coolant, is used to trace the energy transformations of the heat pump. The pressures p1 and p2 in the vaporizer and liquefier, as well as the temperatures Ta, Tb, Te and Tf of the coolant are used to determine the corresponding enthalpy values ha, hb, he and hf. This experiment also measures the heat quantities DQ2 and DQ1 released and absorbed per unit of time. This in turn is used to determine the amount of coolant Dm circulated per unit of time. 88 P 2.6.3.3 P 2.6.3.1 Electricity Table of contents Electricity P3 Electricity P 3.1 P 3.1.1 P 3.1.2 P 3.1.3 P 3.1.4 P 3.1.5 P 3.1.6 P 3.1.7 Electrostatics Basic electrostatics experiments Coulomb's law Lines of electric flux and isoelectric lines Force effects in an electric field Charge distributions on electrical conductors Definition of capacitance Plate capacitor 91–92 93–95 96–97 98–99 100 101 102–103 P 3.6 P 3.6.1 P 3.6.2 P 3.6.3 P 3.6.4 P 3.6.5 P 3.6.6 P 3.6.7 DC and AC circuits Circuit with capacitor Circuit with coil Impedances Measuring-bridge circuits Measuring AC voltages and currents Electrical work and power Electromechanical devices 126 127 128 129 130 131–132 133 P 3.2 P 3.2.1 P 3.2.2 P 3.2.3 P 3.2.4 P 3.2.5 P 3.2.6 Principles of electricity Charge transfer with drops of water Ohm's law Kirchhoff's law Circuits with electrical measuring instruments Conducting electricity by means of electrolysis Experiments on electrochemistry 104 105 106–107 108 109 110 P 3.7 P 3.7.1 P 3.7.2 P 3.7.3 P 3.7.4 P 3.7.5 P 3.7.6 Electromagnetic oscillations and waves Electromagnetic oscillator circuit Decimeter waves Propagation of decimeter waves along lines Microwaves Propagation of microwaves along lines Directional characteristic of dipole radiation 134 135 136 137 138 139 P 3.3 P 3.3.1 P 3.3.2 P 3.3.3 P 3.3.4 Magnetostatics Basic magnetostatics experiments Magnetic dipole moment Effects of force in a magnetic field Biot-Savart's law 111 112 113 114 P 3.8 P 3.8.1 P 3.8.2 P 3.8.3 P 3.8.4 P 3.8.5 Moving charge carriers in a vacuum Tube diode Tube triode Maltese-cross tube Perrin tube Thomson tube 140 141 142 143 144 P 3.4 P 3.4.1 P 3.4.2 P 3.4.3 P 3.4.4 P 3.4.5 P 3.4.6 Electromagnetic induction Voltage impulse Induction in a moving conductor loop Induction by means of a variable magnetic field Eddy currents Transformer Measuring the earth’s magnetic field 115 116 117 118 119–120 121 P 3.9 P 3.9.1 P 3.9.2 P 3.9.3 Electrical conduction in gases Self-maintained and non-self-maintained discharge Gas discharge at reduced pressure Cathode and canal rays 145 146 147 P 3.5 P 3.5.1 P 3.5.2 P 3.5.3 P 3.5.4 Electrical machines Basic experiments on electrical machines Electric generators Electric motors Three-phase machines 122 123 124 125 90 Electricity Electrostatics P 3.1.1 Basic experiments on electrostatics P 3.1.1.1 Basic electrostatics experiments with the field electrometer Basic electrostatics experiments with the field electrometer (P 3.1.1.1) Cat. No. 540 10 540 11 540 12 300 02 300 43 301 01 501 861 501 20 Description Field electrometer Electrostatics demonstration set 1 Electrostatics demonstration set 2 Stand base, V-shape, 20 cm Stand rod, 75 cm Leybold multiclamp Set of 6 croc-clips, polished Connecting lead, Ø 2.5 mm2, 25 cm, red 1 1 1 1 1 1 1 1 The field electrometer is a classic apparatus for demonstrating electrical charges. Its metallized pointer, mounted on needle bearings, is conductively connected to a fixed metal support. When an electrical charge is transferred to the metal support via a pluggable metal plate or a Faraday’s cup, part of the charge flows onto the pointer. The pointer is thus repelled, indicating the charge. P 3.1.1.1 In this experiment, the electrical charges are generated by rubbing two materials together (more precisely, by intensive contact followed by separation), and demonstrated using the field electrometer. This experiment proves that charges can be transferred between different bodies. Additional topics include charging of an electrometer via induction, screening induction via a metal screen and discharge in ionized air. 91 Electrostatics P 3.1.1 Basic experiments on electrostatics P 3.1.1.2 Basic electrostatics experiments with the electrometer amplifier Electricity Basic electrostatics experiments with the electrometer amplifier (P 3.1.1.2) The electrometer amplifier is an impedance converter with an extremely high-ohm voltage input (≥ 1013 Ö) and a low-ohm voltage output (≤ 1 Ö). By means of capacitive connection of the input and using a Faraday’s cup to collect charges, this device is ideal for measuring extremely small charges. Experiments on contact and friction electricity can be conducted with a high degree of reliability. This experiment investigates how charges can be separated through rubbing two materials together. It shows that one of the materials carries positive charges, and the other negative charges, and that the absolute values of the charges are equal. If we measure the charges of both materials at the same time, they cancel each other out. The sign of the charge of a material does not depend on the material alone, but also on the properties of the other material. Cat. No. Description 532 14 562 791 522 27 578 25 578 10 532 16 531 100 541 00 546 12 590 011 542 51 664 152 340 89 501 46 500 424 Electrometer amplifier Plug-in unit 230V/12 V AC/20 W; with female plug Power supply 450 V AC STE Capacitor 01 nF, 630 V STE Capacitor 10 nF, 100 V Connection rod Voltmeter, DC, U ≤ ± 8 V, e.g. Multimeter METRAmax 2 Pair of friction rods Faraday's cup Clamping plug Induction plate Watch glass dish, 40 mm dia. Coupling plug Pair of cables, 1 m, red and blue Connection lead, 50 cm, black P 3.1.1.2 (a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Measuring charges with the electrometer amplifier 92 P 3.1.1.2 (b) 1 1 1 1 1 1 1 1 1 1 1 1 2 1 Electricity Electrostatics P 3.1.2 Coulomb’s law P 3.1.2.1 Confirming Coulomb’s law – measuring with the torsion balance, Schürholz design Confirming Coulomb’s law – measuring with the torsion balance, Schürholz design (P 3.1.2.1) Cat. No. 516 01 516 20 516 04 521 721 501 05 590 13 300 11 532 14 562 791 578 25 578 10 531 100 546 12 590 011 532 16 300 02 471 830 300 42 301 01 313 07 311 03 501 45 500 414 500 424 500 444 501 43 Description Torsion balance after Schürholz Accessories for Coulomb’s law of electrostatics Scale, on stand, 1 m long High voltage power supply 25 kV High voltage cable, 1 m Insulated stand rod, 25 cm Saddle base Electrometer amplifier Plug-in unit 230V/12 V AC/20 W; with female plug STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Voltmeter, DC, U ≤ ± 8 V, e.g. Multimeter METRAmax 2 Faraday's cup Clamping plug Connection rod Stand base, V-shape, 20 cm He-Ne laser 0.2/1 mW max., linearly polarized Stand rod, 47 cm Leybold multiclamp Stopclock I, 30 s/15 min Wooden ruler, 1 m long Pair of cables, 50 cm, red and blue Connection lead, 25 cm, black Connection lead, 50 cm, black Connection lead, 100 cm, black Connection lead, 200 cm, yellow-green 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 According to Coulomb’s law, the force acting between two pointshaped electrical charges Q1 and Q2 at a distance r from each other can be determined using the formula 1 Q ·Q F= · 12 2 4Se0 r where e0 = 8.85 · 10-12 As/Vm (permittivity) The same force acts between two charged fields when the distance r between the sphere midpoints is significantly greater than the sphere diameter, so that the uniform charge distributions of the spheres is undisturbed. In other words, the spheres in this geometry may be treated as points. In this experiment, the coulomb force between two charged spheres is measured using the torsion balance. The heart of this extremely sensitive measuring instrument is a rotating body elastically mounted between two torsion wires, to which one of the two spheres is attached. When the second sphere is brought into close proximity with the first, the force acting between the two charged spheres produces torsion of the wires; this can be indicated and measured using a light pointer. The balance must be calibrated if the force is to be measured in absolute terms. The coulomb force is measured as a function of the distance r. For this purpose, the second sphere, mounted on a stand, is brought close to the first one. Then, at a fixed distance, the charge of one sphere is reduced by half. The measurement can also be carried out using spheres with opposing charges. The charges are measured using an electrometer amplifier connected as a coulomb meter. The aim of the evaluation is to verify the proportionalities 1 F “ 2 and F “ Q1 · Q2 r and to calculate the permittivity e0. P 3.1.2.1 93 Electrostatics P 3.1.2 Coulomb’s law Electricity P 3.1.2.2 Confirming Coulomb’s law – measuring with the force sensor and newton meter Confirming Coulomb’s law with the force sensor and newton meter (P 3.1.2.2) As an alternative to measuring with the torsion balance, the coulomb force between two spheres can also be determined using the force sensor. This device consists of two bending elements connected in parallel with four strain gauges in a bridge configuration; their electrical resistance changes when a load is applied. The change in resistance is proportional to the force acting on the instrument. In this experiment, the force sensor is connected to a newton meter, which displays the measured force directly. No calibration is necessary. The coulomb force is measured as a function of the distance r between the sphere midpoints, the charge Q1 of the first sphere and the charge Q2 of the second sphere. The charges of the spheres are measured using an electrometer amplifier connected as a coulomb meter. The aim of the evaluation is to verify the proportionalities 1 F “ 2 , F “ Q1 and F “ Q2 r and to calculate the permittivity e0. Cat. No. 314 263 337 00 460 82 314 261 314 251 501 16 521 721 501 05 590 13 300 11 532 14 562 791 578 25 578 10 531 100 546 12 590 011 532 16 300 02 300 41 301 01 501 45 500 414 500 424 500 444 501 43 Description Set of bodies for electric charge Trolley 1, 85 g Precision metal rail, 0.5 m Force sensor Newton meter Multicore cable, 6-pole, 1.5 m long High voltage power supply 25 kV High voltage cable, 1 m Insulated stand rod, 25 cm Saddle base Electrometer amplifier Plug-in unit 230 V/12 V AC/20 W; with female plug STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Voltmeter, DC, U ≤ ± 8 V, e. g. Multimeter METRAmax 2 Faraday's cup Clamping plug Connection rod Stand base, V-shape, 20 cm Stand rod, 25 cm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Leybold multiclamp Pair of cables, 50 cm, red and blue Connection lead, 25 cm, black Connection lead, 50 cm, black Connection lead, 100 cm, black Connection lead, 200 cm, yellow-green 1 1 1 1 1 1 94 P 3.1.2.2 Electricity Electrostatics P 3.1.2 Coulomb’s law P 3.1.2.3 Confirming Coulomb’s law – recording and evaluating with CASSY Confirming Coulomb’s law with displacement sensor and CASSY (P 3.1.2.3) Cat. No. 314 263 337 00 460 82 460 95 524 060 Description Set of bodies for electric charge Trolley 1, 85 g Precision metal rail, 0.5 m Clamp rider Force sensor S, ± 1 N 1 1 1 2 1 1 1 1 529 031 524 010 524 200 Displacement sensor Sensor CASSY CASSY Lab 524 031 Current supply box 1 For computer-assisted measuring of the coulomb force between two charged spheres, we can also connect the force sensor to a CASSY interface device via a bridge box. A displacement sensor is additionally required to measure the distance between the charged spheres; this is connected to CASSY via a current source box. This experiment utilizes the software CASSY Lab to record the values and evaluate them. The coulomb force is measured for different charges Q1 and Q2 as a function of the distance r. The charges of the spheres are measured using an electrometer amplifier connected as a coulomb meter. The aim of the evaluation is to verify the proportionality 1 F“ 2 r and to calculate of the permittivity e0. 521 721 501 05 590 13 300 11 532 14 562 791 578 25 578 10 531 100 300 41 546 12 590 011 532 16 300 02 301 01 337 04 301 07 High voltage power supply 25 kV High voltage cable, 1 m Insulated stand rod, 25 cm Saddle base Electrometer amplifier Plug-in unit 230 V/12 V AC / 20 W; with female plug STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Voltmeter, DC, U ≤ ± 8 V, e. g. Multimeter METRAmax 2 Stand rod, 25 cm Faraday's cup Clamping plug Connection rod Stand base, V-shape, 20 cm Leybold multiclamp Set of driving weights Simple bench clamp P 3.1.2.3 1 1 1 1 1* 1* 1* 1* 1* 1 1* 1* 1* 1 1 1 1 Cat. No. 309 48 501 46 500 424 501 43 Description Cord, 10 m Pair of cables, 100 cm, red and blue Connection lead, 50 cm, black Connection lead, 200 cm, yellow-green additionally required: PC with Windows 95/NT or higher * additionally recommended 1+1* 95 P 3.1.2.3 1 1* 1* 1 Electrostatics P 3.1.3 Field lines and equipotential lines P 3.1.3.1 Displaying lines of electric flux Electricity Displaying lines of electric flux (P 3.1.3.1) The space which surrounds an electric charge is in a state which we describe as an electric field. The electric field is also present even when it cannot be demonstrated through a force acting on a sample charge. A field is best described in terms of lines of electric flux, which follow the direction of electric field strength. The orientation of these lines of electric flux is determined by the spatial arrangement of the charges generating the field. In this experiment, small particles in an oil-filled cuvette are used to illustrate the lines of electric flux. The particles align themselves in the electric field to form chains which run along the lines of electric flux. Four different pairs of electrodes are provided to enable electric fields with different spatial distributions to be generated; these electrode pairs are mounted beneath the cuvette, and connected to a high voltage source of up to 10 kV. The resulting patterns can be interpreted as the cross-sections of two spheres, one sphere in front of a plate, a plate capacitor and a spherical capacitor. Cat. No. 541 06 452 111 Description Equipment set E-field lines Overhead projector Famulus alpha 250 501 05 521 70 High voltage cable, 1 m High voltage power supply 10 kV 96 P 3.1.3.1 1 1 2 1 Electricity Electrostatics P 3.1.3 Field lines and equipotential lines P 3.1.3.2 Displaying the equipotential lines of electric fields Displaying the equipotential lines of electric fields (P 3.1.3.2) Cat. No. 545 09 501 861 521 230 Description Electrolytic tank Set of 6 croc-clips, polished Low-voltage power supply, 3, 6, 9, 12 V AC / 3 A Voltmeter, AC, U ≤ 3 V, e. g. Multimeter METRAmax 2 Set of 4 knitting needles Clamping plug Insulated stand rod, 25 cm Stand rod, 25 cm Leybold multiclamp Saddle base Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 1 1 1 2 531 100 510 32 590 011 590 13 300 41 301 01 300 11 501 46 In a two-dimensional cross-section of an electric field, points of equal potential form a line. The direction of these isoelectric lines, just like the lines of electric flux, are determined by the spatial arrangement of the charges generating the field. This experiment measures the isoelectric lines for bodies with different charges. To do this, a voltage is applied to a pair of electrodes placed in an electrolytic tray filled with distilled water. An AC voltage is used to avoid potential shifts due to electrolysis at the electrodes. A voltmeter measures the potential difference between the 0 V electrode and a steel needle immersed in the water. To display the isoelectric lines, the points of equal potential difference are localized and drawn on graph paper. In this way, it is possible to observe and study two-dimensional sections through the electric field in a plate capacitor, a Faraday’s cup, a dipole, an image charge and a slight curve. P 3.1.3.2 Measurement example: equipotential lines around a needle tip 97 Electrostatics P 3.1.4 Effects of force in an electric field P 3.1.4.1 Measuring the force of an electric charge in a homogeneous electric field Electricity Measuring the force of an electric charge in a homogeneous electric field (P 3.1.4.1) In a homogeneous electric field, the force F acting on an elongated charged body is proportional to the total charge Q and the electric field strength E. Thus, the formula F=Q·E applies. In this experiment, the greatest possible charge Q is transferred to an electrostatic spoon from a plastic rod. The electrostatic spoon is within the electric field of a plate capacitor and is aligned parallel to the plates. To verify the proportional relationship between the force and the field strength, the force F acting on the electrostatic spoon is measured at a known plate distance d as a function of the capacitor voltage U. The electric field E is determined using the equation U E= d The measuring instrument in this experiment is a current balance, a differential balance with light-pointer read-out, in which the force to be measured is compensated by the spring force of a precision dynamometer. Cat. No. 516 32 314 081 314 263 541 04 541 21 544 22 300 75 521 70 501 05 471 830 441 53 300 01 300 02 300 11 300 42 301 01 500 414 Description Current balance with conductors Precision dynamometer, 0.01 N Set of bodies for electric charge Plastic rod Leather Parallel plate capacitor Laboratory stand I High voltage power supply 10 kV High voltage cable, 1 m He-Ne laser 0.2/1 mW max., linearly polarized Translucent screen Stand base, V-shape, 28 cm Stand base, V-shape, 20 cm Saddle base Stand rod, 47 cm Leybold multiclamp Connection lead, 25 cm, black 98 P 3.1.4.1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 Electricity Electrostatics P 3.1.4 Effects of force in an electric field P 3.1.4.2 Kirchhoff’s voltage balance: Measuring the force between two charged plates of a plate capacitor P 3.1.4.3 Measuring the force between a charged sphere and a metal plate Measuring the force between a charged sphere and a metal plate (P 3.1.4.3) Cat. No. 516 37 516 31 314 251 314 261 314 265 501 16 521 70 501 05 300 42 300 02 301 01 541 04 541 21 500 410 500 420 500 440 Description Electrostatic accessories Vertically adjustable stand Newton meter Force sensor Support for conductor loops Multicore cable, 6-pole, 1.5 m long High voltage power supply 10 kV High voltage cable, 1 m Stand rod, 47 cm Stand base, V-shape, 20 cm Leybold multiclamp Plastic rod Leather Connection lead, 25 cm, yellow/green Connection lead, 50 cm, yellow/green Connection lead, 100 cm, yellow/green 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 As an alternative to measurement with the current balance, the force in an electric field can also be measured using a force sensor connected to a newton meter. The force sensor consists of two bending elements connected in parallel with four strain gauges in a bridge configuration; their electrical resistance changes when a load is applied. The change in resistance is proportional to the force acting on the sensor. The newton meter displays the measured force directly. In the first experiment Kirchhoff’s voltage balance is set up in order to measure the force 1 U2 F = · e0 · 2 · A 2 d where e0 = 8.85 · 10-12 As/Vm (permittivity) acting between the two charged plates of a plate capacitor. At a given area A, the measurement is conducted as a function of the plate distance d and the voltage U. The aim of the evaluation is to confirm the proportionalities 1 F “ 2 and F “ U2 d and to determine the permittivity e0. The second experiment consists of a practical investigation of the principle of the image charge. Here, the attractive force acting on a charged sphere in front of a metal plate is measured. This force is equivalent to the force of an equal, opposite charge at twice the distance 2d. Thus, it is described by the formula 1 Q2 F= · 4Se0 (2d)2 First, the force for a given charge Q is measured as a function of the distance d. The measurement is then repeated with half the charge. The aim of the evaluation is to confirm the proportionalities 1 F “ 2 and F “ Q2. d 99 P 3.1.4.2 1 2 P 3.1.4.3 1 Electrostatics P 3.1.5 Charge distributions on electrical conductors P 3.1.5.1 Investigating the charge distribution on the surface of electrical conductors P 3.1.5.2 Electrostatic induction with the hemispheres after Cavendish Electricity Electrostatic induction with the hemispheres after Cavendish (P 3.1.5.2) In static equilibrium, the interior of a metal conductor or a hollow body contains neither electric fields nor free electron charges. On the outer surface of the conductor, the free charges are distributed in such a way that the electric field strength is perpendicular to the surface at all points, and all points have equal potential. In the first experiment, an electric charge is collected from a charged hollow metal sphere using a charge spoon, and measured using a coulomb meter. It becomes apparent that the charge density is greater, the smaller the bending radius of the surface is. This experiment also shows that no charge can be taken from the interior of the hollow body. The second experiment reconstructs a historic experiment first performed by Cavendish. A metal sphere is mounted on an insulated base. Two hollow hemispheres surround the sphere completely, but without touching it. When one of the hemispheres is charged, the charge distributes itself uniformly over both hemispheres, while the inside sphere remains uncharged. If the inside sphere is charged and then surrounded by the hemispheres, the two hemispheres again show equal charges, and the inside sphere is uncharged. Cat. No. 543 07 543 02 543 05 546 12 542 52 521 70 501 05 532 14 562 791 578 25 578 10 531 100 340 89 590 011 532 16 540 52 300 11 300 41 301 01 590 13 501 861 501 45 500 444 500 424 501 43 Description Conical conductor on insulated rod Sphere on insulated rod Pair of hemispheres Faraday's cup Metal plate on insulating rod High voltage power supply 10 kV High voltage cable, 1 m Electrometer amplifier Plug-in unit 230 V/12 V AC / 20 W; with female plug STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Voltmeter, DC, U ≤ ± 8 V, e. g. Multimeter METRAmax 2 Coupling plug Clamping plug Connection rod Demonstration insulator Saddle base Stand rod, 25 cm Leybold multiclamp Insulated stand rod, 25 cm Set of 6 croc-clips, polished Pair of cables, 50 cm, red and blue Connection lead, 100 cm, black Connection lead, 50 cm, black Connection lead, 200 cm, yellow-green 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 2 1 1 1 1 1 1 1 1 1 1 100 P 3.1.5.2 P 3.1.5.1 Electricity Electrostatics P 3.1.6 Definition of capacitance P 3.1.6.1 Determining the capacitance of a sphere in free space P 3.1.6.2 Determining the capacitance of a sphere in front of a metal plate Determining the capacitance of a sphere in free space (P 3.1.6.1) Cat. No. 546 12 543 00 587 66 521 70 501 05 532 14 562 791 578 25 578 10 531 100 590 011 532 16 300 11 590 13 Description Faraday's cup Set of 3 conducting spheres Reflection plate, 50 cm x 50 cm High voltage power supply 10 kV High voltage cable, 1 m Electrometer amplifier Plug-in unit 230 V/12 V AC / 20 W; with female plug STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Voltmeter, DC, U ≤ ± 8 V, e. g. Multimeter METRAmax 2 Clamping plug Connection rod Saddle base Insulated stand rod, 25 cm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 3 1 The potential difference U of a charged conductor in an insulated mounting in free space with reference to an infinitely distant reference point is proportional to the charge Q of the body. We can express this using the relationship Q=C·U and call C the capacitance of the body. Thus, for example, the capacitance of a sphere with the radius r in a free space is C = 4Se0 · r because the potential difference of the charged sphere with respect to an infinitely distant reference point is 1 Q U= · 4Se0 r where e0 = 8.85 · 10-12 As/Vm (permittivity). The first experiment determines the capacitance of a sphere in a free space by charging the sphere with a known high voltage U and measuring its charge Q using an electrometer amplifier connected as a coulomb meter. The measurement is conducted for different sphere radii r. The aim of the evaluation is to verify the proportionalities Q “ U and C “ r. The second experiment shows that the capacitance of a body also depends on its environment, e. g. the distance to other earthed conductors. In this experiment, spheres with the radii r are arranged at a distance s from an earthed metal plate and charged using a high voltage U. The capacitance of the arrangement is now r C = 4Se0 · r · 1 + . 2s 501 861 311 77 500 444 500 424 500 414 501 45 501 43 300 42 Set of 6 croc-clips, polished Steel tape measure, 2 m Connection lead, 100 cm, black Connection lead, 50 cm, black Connection lead, 25 cm, black Pair of cables, 50 cm, red and blue Connection lead, 200 cm, yellow-green 1 1 1 1 1 I Stand rod, 47 cm I I1 P 3.1.6.2 1 1 2 1 1 1 1 P 3.1.6.1 ( ) The aim of the evaluation is to confirm the proportionality between the charge Q and the potential difference U at any given distance s between the sphere and the metal plate. 101 Electrostatics P 3.1.7 Plate capacitor Electricity P 3.1.7.1 Determining the capacitance of a plate capacitor – measuring the charge with the electrometer amplifier P 3.1.7.2 Parallel and series connection of capacitors – measuring the charge with the electrometer amplifier Determining the capacitance of a plate capacitor – measuring the charge with the electrometer amplifier (P 3.1.7.1) A plate capacitor is the simplest form of a capacitor. Its capacitance depends on the plate area A and the plate spacing d. The capacitance increases when an insulator with the dielectric constant er is placed between the two plates. The total capacitance is A C = ere0 · d where e0 = 8.85 · 10-12 As/Vm (permittivity). In the first experiment, this relationship is investigated using a demountable capacitor assembly with variable geometry. Capacitor plates with the areas A = 40 cm2 and A = 80 cm2 can be used, as well as various plate-type dielectrics. The distance can be varied in steps of one millimeter. The second experiment determines the total capacitance C of the demountable capacitor with the two plate pairs arranged at a fixed distance and connected first in parallel and then in series, compares these with the individual capacitances C1 and C2 of the two plate pairs. The evaluation confirms the relationship C = C1 + C2 for parallel connection and 1 1 1 = + C C1 C2 for serial connection. Cat. No. 544 23 522 27 504 48 531 100 531 100 532 14 578 25 578 10 532 16 501 45 501 46 Description Demountable capacitor Power supply 450 V AC Two-way switch Voltmeter, DC, U = ± 8 V, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 300 V, e. g. Multimeter METRAmax 2 Electrometer amplifier STE capacitor 1 nF, 630 V STE capacitor 10 nF, 100 V Connection rod Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, red and blue 1 1 1 1 1 1 1 1 1 3 2 102 P 3.1.7.2 1 1 1 1 1 1 1 1 1 4 2 P 3.1.7.1 Electricity Electrostatics P 3.1.7 Plate capacitor P 3.1.7.3 Determining the capacitance of a plate capacitor – measuring the charge with the I-measuring amplifier D Determining the capacitance of a plate capacitor – measuring the charge with the I-measuring amplifier D (P 3.1.7.3) Cat. No. 544 22 521 65 504 48 532 00 531 100 531 712 536 221 500 421 501 45 501 46 Description Parallel plate capacitor DC power supply 0 .... 500 V Two-way switch I-Measuring amplifier D Voltmeter, DC , U ≤ 10 V, e. g. Multimeter METRAmax 2 Voltmeter, DC , U ≤ 500 V, e. g. Multimeter METRAmax 3 Measuring resister 100 MV Connecting lead, 50 cm, red Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, red and blue 1 1 1 1 1 1 1 1 2 1 Calculation of the capacitance of a plate capacitor using the formula A C = e0 · d A: plate area d: plate spacing where e0 = 8.85 · 10-12 As/Vm (permittivity) ignores the fact that part of the electric field of the capacitor extends beyond the edge of the plate capacitor, and that consequently a greater charge is stored for a specific potential difference between the two capacitors. For example, for a plate capacitor grounded on one side and having the area A = S · r2 the capacitance is given by the formula S · r2 Sr C = e0 + 3.7724 · r + r · ln + ... d d P 3.1.7.3 ( ( ) ) In this experiment, the capacitance C of a plate capacitor is measured as a function of the plate spacing d with the greatest possible accuracy. This experiment uses a plate capacitor with a plate radius of 13 cm and a plate spacing which can be continuously varied between 0 and 70 mm. The aim of the evaluation is to plot the measured values in the form 1 C=f d () and compare them with the values to be expected according to theory. 103 Fundamentals of electricity P 3.2.1 Charge transfer with drops of water P 3.2.1.1 Generating an electric current through the motion of charged drops of water Electricity Generating an electric current through the motion of charged drops of water (P 3.2.1.1) Each charge transport is an electric current. The electrical current strength (or more simply the “current”) DQ I= Dt is the charge DQ transported per unit of time Dt. For example, in a metal conductor, DQ is given by the number DN of free electrons which flow through a specific conductor cross-section per unit of time Dt. We can illustrate this relationship using charged water droplets. In the experiment, charged water drops drip out of a burette at a constant rate . DN N= Dt N: number of water drops into a Faraday’s cup, and gradually charge the latter. Each individual drop of water transports approximately the same charge q. The total charge Q in the Faraday’s cup is measured using an electrometer amplifier connected as a coulomb meter. This charge shows a step-like curve as a function of the time t, as can be recorded using a YT recorder. At a high drip rate N, a very good approximation is . Q = N · q · t. The current is then . I=N·q Cat. No. 665 843 546 12 522 27 532 14 532 16 578 25 578 26 578 10 578 22 531 100 575 703 Description Burette, 10 ml: 0.05, with lateral stopcock, clear glass, Schellbach blue line Faraday's cup Power supply 450 V DC Electrometer amplifier Connection rod STE capacitor 1 nF, 630 V STE capacitor 2.2 nF, 160 V STE capacitor 10 nF, 100 V STE capacitor 100 pF, 630 V Voltmeter, DC, U = ± 8 V, e. g. Multimeter METRAmax 2 YT-recorder, single channel Beaker, 50 ml, ss, plastic Stand base MF Stand rod, 50 cm, 10 mm dia. Stand rod, 25 cm, 10 mm dia. Leybold multiclamp Universal clamp, 0 ... 80 mm dia. Constantan wire, 100 m, 0.25 mm Ø Set of 6 two-way plug adapters, red Set of 6 croc-clips, polished Connection lead, 25 cm, blue Connection lead, 50 cm, black Pair of cables, 50 cm, red and blue Connection lead, 100 cm, black Pair of cables, 1 m, red and blue *additionally recommended 664 120 301 21 301 27 301 26 301 01 666 555 550 41 501 641 501 861 500 412 500 424 501 45 500 444 501 46 104 P 3.2.1.1 1 1 1 1 1 1 1 1 1 1 1* 1 2 1 1 1 1 1 1 1 1 1 2 2 1 Electricity Fundamentals of electricity P 3.2.2 Ohm’s law P 3.2.2.1 Verifying Ohm’s law Verifying Ohm’s law (P 3.2.2.1) Cat. No. 550 57 521 45 531 100 531 100 501 46 501 33 501 23 Description Apparatus for resistance measurements DC power supply 0....+/- 15 V Ammeter, DC, I ≤ 3 A, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 15 V, e. g. Multimeter METRAmax 2 Pair of cables, 1 m, red and blue Connecting lead, Ø 2.5 mm2, 100 cm, black Connecting lead, Ø 2.5 mm2, 25 cm, black 1 1 1 1 1 3 1 In circuits consisting of metal conductors, Ohm’s law U=R·I represents a very close approximation of the actual circumstances. In other words, the voltage drop U in a conductor is proportional to the current I through the conductor. The proportionality constant R is called the resistance of the conductor. For the resistance, we can say s R=U · A r: resistivity of the conductor material, s: length of wire, A: cross-section of wire This experiment verifies the proportionality between the current and voltage for metal wires of different materials, thicknesses and lengths, and calculates the resistivity of each material. P 3.2.2.1 105 Fundamentals of electricity P 3.2.3 Kirchhoff’s laws Electricity P 3.2.3.1 Measuring current and voltage at resistors connected in parallel and in series P 3.2.3.2 Voltage division with a potentiometer P 3.2.3.3 Principle of a Wheatstone bridge Measuring current and voltage at resistors connected in parallel and in series (P 3.2.3.1) Kirchhoff’s laws are of fundamental importance in calculating the component currents and voltages in branching circuits. The socalled “node rule” states that the sum of all currents flowing into a particular junction point in a circuit is equal to the sum of all currents flowing away from this junction point. The “mesh rule” states that in a closed path the sum of all voltages through the loop in any arbitrary direction of flow is zero. Kirchhoff’s laws are used to derive a system of linear equations which can be solved for the unknown current and voltage components. The first experiment examines the validity of Kirchhoff’s laws in circuits with resistors connected in parallel and in series. The result demonstrates that two resistors connected in series have a total resistance R R = R1 + R2 while for parallel connection of resistors, the total resistance R is 1 1 1 = + R R1 R2 In the second experiment, a potentiometer is used as a voltage divider in order to tap a lower voltage component U1 from a voltage U. U is present at the total resistance of the potentiometer. In a no-load, zero-current state, the voltage component R U1 = 1 · U R can be tapped at the variable component resistor R1. The relationship between U1 and R1 at the potentiometer under load is no longer linear. The third experiment examines the principle of a Wheatstone bridge, in which “unknown” resistances can be measured through comparison with “known” resistances. Cat. No. 576 74 Description Plug-in board A4 STE resistor 47 Ö, 2 W STE resistor 100 Ö, 2 W STE resistor 150 Ö, 2 W STE resistor 220 Ö, 2 W STE resistor 330 Ö, 2 W STE resistor 470 Ö, 2 W STE resistor 1 kÖ, 2 W STE resistor 5.6 kÖ, 2 W STE resistor 10 kÖ, 0.5 W STE resistor 100 kÖ, 0.5 W STE potentiometer 1 kÖ, 1 W STE potentiometer 220 Ö, 3 W Set of 10 bridging plugs DC power supply 0 .... +/- 15 V Ammeter, DC, I ≤ 1 A, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 15 V, e. g. Multimeter METRAmax 2 Pair of cables, 50 cm, red and blue 1 1 1 2 1 577 28 577 32 577 34 577 36 577 38 577 40 577 44 577 53 577 56 577 68 577 92 577 90 501 48 521 45 531 100 531 100 501 45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 531 100 I Ammeter, DC, I <= 10 µA, cero point middle, e.g. I I Multimeter METRAmax 2 I I I I I I I I I1 106 P 3.2.3.3 1 1 2 1 1 1 1 1 2 P 3.2.3.2 P 3.2.3.1 Electricity Fundamentals of electricity P 3.2.3 Kirchhoff’s laws P 3.2.3.4 Determining resistances using a Wheatstone bridge Determining resistances using a Wheatstone bridge (P 3.2.3.4) Cat. no. 536 02 536 121 536 131 536 141 536 776 536 777 536 778 536 779 521 45 531 13 501 28 501 46 Description Demonstration bridge, 1 m long Measuring resistor 10 Ö, 4 W Measuring resistor 100 Ö, 4 W Measuring resistor 1 kÖ, 4 W Resistance decade 0...1 kÖ Resistance decade 0...100 Ö Resistance decade 0...10 Ö Resistance decade 0...1 Ö DC power supply 0....+/- 15 V Ammeter, DC, I ≤ 3 mA, D I = 1 mA Zero point center, Galvanometer C.A 403 Connecting lead, Ø 2,5 mm2, 50 cm, black Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 1 1 1 3 1 In modern measuring practice, the bridge configuration developed in 1843 by Ch. Wheatstone is used almost exclusively. In this experiment, a voltage U is applied to a 1 m long measuring wire with a constant cross-section. The ends of the wire are connected to an unknown resistor Rx and a variable resistor R arranged behind it, whose value is known precisely. A sliding contact divides the measuring wire into two parts with the lengths s1 and s2. The slide contact is connected to the node between Rx and R via an ammeter which is used as a zero indicator. Once the current has been regulated to zero, the relationship s Rx = 1 · R s2 P 3.2.3.4 applies. Maximum accuracy is achieved by using a symmetrica experiment setup, i. e. when the slide contact over the measuring wire is set in the middle position so that the two sections s1 and s2 are the same length. Circuit diagram of Wheatstone bridge 107 Principles of electricity P 3.2.4 Circuits with electrical measuring instruments P 3.2.4.1 The ammeter as an ohmic resistor in a circuit P 3.2.4.2 The voltmeter as an ohmic resistor in a circuit Electricity The ammeter as an ohmic resistor in a circuit (P 3.2.4.1) One important consequence of Kirchhoff’s laws is that the internal resistance of an electrical measuring instrument affects the respective current or voltage measurement. Thus, an ammeter increases the overall resistance of a circuit by the amount of its own internal resistance and thus measures a current value which is too low whenever the internal resistance is above a negligible level. A voltmeter measures a voltage value which is too low when its internal resistance is not great enough with respect to the resistance at which the voltage drop is to be measured. In the first experiment, the internal resistance of an ammeter is determined by measuring the voltage which drops at the ammeter during current measurement. It is subsequently shown that the deflection of the ammeter pointer is reduced by half, or that the current measuring range is correspondingly doubled, by connecting a second resistor equal to the internal resistance in parallel to the ammeter. The second experiment determines the internal resistance of a voltmeter by measuring the current flowing through it. In this experiment, the measuring range is extended by connecting a second resistor with a value equal to the internal resistance to the voltmeter in series. Cat. No. 576 74 577 33 577 52 577 71 577 75 501 48 521 45 531 51 501 45 Description Plug-in board A4 STE resistor 82 V, 2 W STE resistor 4.7 kV, 2 W STE resistor 220 kV, 0.5 W STE resistor 680 kV, 0.5 W Set of 10 bridging plugs DC power supply 0....+/- 15 V Multimeter MA 1 H Pair of cables, 50 cm, red and blue 1 3 1 1 1 2 3 108 P 3.2.4.2 1 1 1 1 1 1 2 3 P 3.2.4.1 Electricity Fundamentals of electricity P 3.2.5 Conducting electricity by means of electrolysis P 3.2.5.1 Determining the Faraday constant Determining the Faraday constant (P 3.2.5.1) Cat. No. 664 350 382 36 531 83 521 45 531 100 649 45 674 792 501 45 501 46 Description Water electrolysis unit Thermometer, -10 to + 40 °C Joule and wattmeter DC power supply 0....+/- 15 V Voltmeter, DC, U ≤ 30 V, e. g. Multimeter METRAmax 2 Tray, 6 x 5 RE Sulfuric acid, diluted, 500 ml Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 2 1 In electrolysis, the processes of electrical conduction entails liberation of material. The quantity of liberated material is proportional to the transported charge Q flowing through the electrolyte. This charge can be calculated using the Faraday constant F, a universal constant which is related to the unit charge e by means of Avogadro’s number NA. F = NA · e When we insert the molar mass n for the material quantity and take the valence z of the separated ions into consideration, we obtain the relationship Q=n·F·z In this experiment, a specific quantity of hydrogen is produced in an electrolysis apparatus after Hofmann to determine the Faraday constant. The valance of the hydrogen ions is z = 1. The molar mass n of the liberated hydrogen atoms is calculated using the laws of ideal gas on the basis of the volume V of the hydrogen collected at an external pressure p and room temperature T: pV n=2· RT J where R = 8.314 (universal gas constant) mol · K At the same time, the electric work W is measured which is expended for electrolysis at a constant voltage U0. The transported charge quantity is then Q= W . U0 P 3.2.5.1 109 Fundamentals of electricity P 3.2.6 Experiments on electrochemistry P 3.2.6.1 Generating electric current with a Daniell cell P 3.2.6.2 Measuring the voltage at simple galvanic elements P 3.2.6.2 Determining the standard potentials of corresponding redox pairs Electricity Measuring the voltage at galvanic elements (P 3.2.6.2) In galvanic cells, electrical energy is generated using an electrochemical process. The electrochemistry workplace enables you to investigate the physical principles which underlie such processes. In the first experiment, a total of four Daniell cells are assembled. These consist of one half-cell containing a zinc electrode in a ZnSO4 solution and one half-cell containing a copper electrode in a CuSO4 solution. The voltage produced by multiple cells connected in series is measured and compared with the voltage from a single cell. The current of a single cell is used to drive an electric motor. The second experiment combines half-cells of corresponding redox pairs of the type metal/metal cation to create simple galvanic cells. For each pair, the object is to determine which metal represents the positive and which one the negative pole, and to Cat. No. Description 664 394 664 395 661 125 Electrochemistry workplace measuring unit Electrochemistry working place Set of chemicals for electrochemistry measure the voltage between the half-cells. From this, a voltage series for the corresponding redox pairs can be developed. The third experiment uses a platinum electrode in 1-mol hydrochloric acid as a simple standard hydrogen electrode in order to permit direct measurement of the standard potentials of corresponding redox pairs of the type metal/metal cation and nonmetallic anion/non-metallic substance directly. 110 P 3.2.6.1-3 1 1 1 Electricity Magnetostatics P 3.3.1 Basic experiments on magnetostatics P 3.3.1.1 Displaying lines of magnetic flux P 3.3.1.2 Basics of electromagnetism Deflection of a conductor by a permanent magnet (P 3.3.1.2) Cat. No. 560 70 560 15 513 11 513 51 510 21 510 12 514 72 514 73 452 111 Description Magnetic field demonstration set Equipment for electromagnetism Magnetic needle Base for magnetic needle Horse-shoe magnet, with yoke Pair of round magnets Shaker for iron filings Iron filings 250 g Overhead projector Famulus alpha 250 1 1 1 1 1 1 1 1 1 521 55 300 02 300 43 301 01 666 555 540 52 300 11 501 26 501 30 501 31 501 35 501 36 High current power supply Stand base, V-shape, 20 cm Stand rod, 75 cm Leybold multiclamp Universal clamp, 0 ... 80 mm dia. Demonstration insulator Saddle base Connecting lead, Ø 2,5 mm2, 50 cm, blue Connecting lead, Ø 2.5 mm2, 100 cm, red Connecting lead, Ø 2.5 mm2, 100 cm, blue Connecting lead, Ø 2.5 mm2, 200 cm, red Connecting lead, Ø 2.5 mm2, 200 cm, blue 1 1 1 1 3 1 2 2 1 Magnetostatics studies the spatial distribution of magnetic fields in the vicinity of permanent magnets and stationary currents as well as the force exerted by a magnetic field on magnets and currents. Basic experiments on this topic can be carried out without complex experiment setups. In the first experiment, magnetic fields are observed by spreading iron filings over a smooth surface so that they align themselves with the lines of magnetic flux. By this means it becomes possible to display the magnetic field of a straight conductor, the magnetic field of a conductor loop and the magnetic field of a coil. The second topic combines a number of fundamental experiments on electromagnetic phenomena. First, the magnetic field surrounding a current-carrying conductor is illustrated. Then the force exerted by two current-carrying coils on each other and the deflection of a current-carrying coil in the magnetic field of a second coil are demonstrated. 1 1 1 1 P 3.3.1.2 P 3.3.1.1 Displaying lines of magnetic flux (P 3.3.1.1) 111 Magnetostatics P 3.3.2 Magnetic dipole moment Electricity P 3.3.2.1 Measuring the magnetic dipole moments of long magnetic needles Measuring the magnetic dipole moments of long magnetic needles (P 3.3.2.1) Although only magnetic dipoles occur in nature, it is useful in some cases to work with the concept of highly localized “magnetic charges”. Thus, we can assign pole strengths or “magnetic charges” qm to the pole ends of elongated magnetic needles on the basis of their length d and their magnetic moment m: m qm = d The pole strength is proportional to the magnetic flux F: F = m0 · q m Vs where m0 = 4S · 10-7 (permeability) Am Thus, for the spherical surface with a small radius r around the pole (assumed as a point source), the magnetic field is 1 q B= · m 4Sm0 r2 At the end of a second magnetic needle with the pole strength q’m, the magnetic field exerts a force F = q’m · B and consequently 1 q · q’ F= · m 2 m 4Sm0 r In formal terms, this relationship is equivalent to Coulomb’s law governing the force between two electrical charges. This experiment measures the force F between the pole ends of two magnetized steel needles using the torsion balance. The experiment setup is similar to the one used to verify Coulomb’s law. The measurement is initially carried out as a function of the distance r of the pole ends. To vary the pole strength qm, the pole ends are exchanged, and multiple steel needles are mounted next to each other in the holder. Cat. No. 516 01 510 50 516 21 516 04 450 60 450 51 460 20 521 210 Description Torsion balance after Schürholz Bar magnet 60 x 13 x 5 mm Accessories for magnetostatics Scale, on stand, 1 m long Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC / 30 W Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp 300 02 300 42 301 01 112 P 3.3.2.1 1 1 1 1 1 1 1 1 1 1 1 Electricity Magnetostatics P 3.3.3 Effects of force in a magnetic field P 3.3.3.1 Measuring the force acting on current-carrying conductors in the field of a horseshoe magnet P 3.3.3.2 Measuring the force acting on current-carrying conductors in a homogeneous magnetic field – Recording with CASSY P 3.3.3.3 Measuring the force acting on current-carrying conductors in the magnetic field of an air coil – Recording with CASSY P 3.3.3.4 Basic measurements for the electrodynamic definition of the ampere Measuring the force acting on current-carrying conductors in a homogeneous magnetic field – Recording with CASSY (P 3.3.3.2) Cat. No. 510 22 Description Large horse-shoe magnet, with yoke 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 562 11 562 14 562 25 314 265 516 34 516 244 516 249 516 33 516 31 521 55 521 50 314 251 314 261 524 010 524 060 U-core with yoke Coil with 500 turns Pole-shoe yoke Support for conductor loops Conductor loops for force measurement Field coil, diameter 120 mm Stand for coils and tubes Set of conductors for Ampere definition Vertically adjustable stand Current source, DC, I ≤ 20 A, e. g. High current power supply Current source, DC, I ≤ 5 A, e.g. AC/DC power supply 0....15 V Newtonmeter Force sensor Sensor CASSY Force sensor S, ± 1 N 1 1 1 1 1 1 1 1 524 043 524 200 501 16 300 02 300 42 301 01 501 25 501 26 501 30 501 31 Sensor box - 30 Amperes CASSY Lab Multicore cable, 6-pole, 1.5 m long Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Connecting lead, Ø 2,5 mm2, 50 cm, red Connecting lead, Ø 2,5 mm2, 50 cm, blue Connecting lead, Ø 2.5 mm2, 100 cm, red Connecting lead, Ø 2.5 mm2, 100 cm, blue additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 To measure the force acting on a current-carrying conductor in a magnetic field, conductor loops are attached to a force sensor. The force sensor contains two bending elements arranged in parallel with four strain gauges connected in a bridge configuration; their resistance changes in proportion to the force when a strain is applied. The force sensor is connected to a newton meter, or alternatively to the CASSY computer interface device via a bridge box. When using CASSY a 30 ampere box is recommended for current measurement. In the first experiment, the conductor loops are placed in the magnetic field of a horseshoe magnet. This experiment measures the force F as a function of the current I, the conductor length s and the angle a between the magnetic field and the conductor, and reveals the relationship F = I · s · B sin a In the second experiment, a homogeneous magnetic field is generated using an electromagnet with U-core and pole-piece attachment. This experiment measures the force F as a function of the current I. The measurement results for various conductor lengths s are compiled and evaluated in a graph. The third experiment uses an air coil to generate the magnetic field. The magnetic field is calculated from the coil parameters and compared with the values obtained from the force measurement. The object of the fourth experiment is the electrodynamic definition of the ampere. Here, the current is defined on the basis of the force exerted between two parallel conductors of infinite length which carry an identical current. When r represents the distance between the two conductors, the force per unit of length of the conductor is: l2 F = m0 · s 2S · r This experiment uses two conductors approx. 30 cm long, placed just a few millimeters apart. The forces F are measured as a function of the different current levels I and distances r. 113 P 3.3.3.2 P 3.3.3.3 P 3.3.3.4 P 3.3.3.1 Magnetostatics P 3.3.4 Biot-Savart’s law Electricity P 3.3.4.1 Measuring the magnetic field for a straight conductor and for circular conductor loops P 3.3.4.2 Measuring the magnetic field of an air coil P 3.3.4.3 Measuring the magnetic field of a pair of coils in the Helmholtz configuration Measuring the magnetic field for a straight conductor and for circular conductor loops (P 3.3.4.1) In principle, it is possible to calculate the magnetic field of any current-carrying conductor using Biot and Savart’s law. However, analytical solutions can only be derived for conductors with certain symmetries, e. g. for an infinitely long straight wire, a circular conductor loop and a cylindrical coil. Biot and Savart’s law can be verified easily using these types of conductors. In the first experiment, the magnetic field of a long, straight conductor is measured for various currents I as a function of the distance r from the conductor. The result is a quantitative confirmation of the relationship m l B= 0 · 2S r In addition, the magnetic fields of circular coils with different radii R are measured as a function of the distance x from the axis through the center of the coil. The measured values are compared with the values which are calculated using the equation m l · R2 B= 0 · 2 + x2)3 2 (R 2 All measurements can be carried out using an axial B-probe. This device contains a Hall sensor which is extremely sensitive to fields parallel to the probe axis. A tangential B-probe, in which the Hall sensor is sensitive perpendicular to the probe axis, is recommended for further investigations. The second experiment investigates the magnetic field of an air coil in which the length L can be varied for a constant number of turns N. For the magnetic field the relationship N B = m0 · l · L applies. Cat. No. 516 235 516 242 516 249 555 604 Description Set of 4 current conductors Coil with variable number of turns per unit length Stand for coils and tubes Pair of Helmholtz coils Teslameter Axial B-probe Tangential B-probe Multicore cable, 6-pole, 1.5 m long High current power supply Small optical bench Holder for plug-in elements Leybold multiclamp Stand base, V-shape, 28 cm Saddle base Set of 6 two-way plug adapters, black Connecting lead, Ø 2,5 mm2, 50 cm, blue Connecting lead, Ø 2.5 mm2, 100 cm, red Connecting lead, Ø 2.5 mm2, 100 cm, blue 1 1 1 1 1 1 1* 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 516 62 516 61 516 60 501 16 521 55 460 43 460 21 301 01 300 01 300 11 501 644 501 26 501 30 501 31 1 1 * additionally recommended The third experiment examines the homogeneity of the magnetic field in a pair of Helmholtz coils. The magnetic field along the axis through the coil centers is recorded in several measurement series; the spacing a between the coils is varied from measurement series to measurement series. When a is equal to the coil radius, the magnetic field is essentially independent of the location x on the coil axis. 114 P 3.3.4.3 1 1 1 P 3.3.4.2 P 3.3.4.1 Electricity Electromagnetic induction P 3.4.1 Voltage impulse P 3.4.1.1 Generating a voltage surge in a conductor loop with a moving permanent magnet Generating a voltage surge in a conductor loop with a moving permanent magnet (P 3.4.1.1) Cat. No. 510 11 562 13 562 14 562 15 524 010 524 200 501 46 Description Round magnet Coil with 250 turns Coil with 500 turns Coil with 1000 turns Sensor CASSY CASSY Lab Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 3 1 1 1 1 1 1 1 Each change in the magnetic flux F through a conductor loop induces a voltage U, which has a level proportional to the change in the flux. Such a change in the flux is caused e. g. when a permanent magnet is moved inside a fixed conductor loop. In this case, it is common to consider not only the time-dependent voltage dF U= dt but also the voltage surge t2 t1 P 3.4.1.1 ∫ U(t)dt = F(t1) – F(t2) This corresponds to the difference in the magnetic flux densities before and after the change. In this experiment, the voltage surge is generated by manually inserting a bar magnet into an air coil, or pulling it out of a coil. The curve of the voltage U over time is measured and the area inside the curve is evaluated. This is always equal to the flux F of the permanent magnet inside the air coil independent of the speed at which the magnet is moved, i. e. proportional to the number of turns of the coil for equal coil areas. 115 Electromagnetic induction P 3.4.2 Induction in a moving conductor loop P 3.4.2.1 Measuring the induction voltage in a conductor loop moved through a magnetic field Electricity Measuring the induction voltage in a conductor loop moved through a magnetic field (P 3.4.2.1) When a conductor loop with the constant width b is withdrawn from a homogeneous magnetic field B with the speed dx v= dt the magnetic flux changes over the time dt by the value dF = -B · b · dx This change in flux induces the voltage U=B·b·v in the conductor loop. In this experiment, a slide on which induction loops of various widths are mounted is moved between the two pole pieces of a magnet. The object is to measure the induction voltage U as a function of the magnetic flux density B, the width b and the speed v of the induction loops. The aim of the evaluation is to verify the proportionalities U “ B, U “ b and U “ v. Cat. No. 516 40 510 48 347 35 347 36 532 13 Description Induction apparatus Pair of magnets, cylindrical Experiment motor Control unit for experiment motor Microvoltmeter Induction voltage in a moved conductor loop 116 P 3.4.2.1 1 6 1 1 1 Electricity Electromagnetic induction P 3.4.3 Induction by means of a variable magnetic field P 3.4.3.1 Measuring the induction voltage in a conductor loop for a variable magnetic field Measuring the induction voltage in a conductor loop for a variable magnetic field (P 3.4.3.1) Cat. No. 516 249 516 244 516 241 521 56 524 040 524 010 524 043 524 200 500 422 501 46 Description Stand for coils and tubes Field coil, diameter 120 mm Set of induction coils Triangular wave-form power supply mV-Box Sensor-CASSY Sensor box - 30 Amperes CASSY Lab Connection lead, 50 cm, blue Pair of cables, 50 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 2 1 A change in the homogeneous magnetic field B inside a coil with N1 windings and the area A1 over time induces the voltage dB U = N1 · A1 · . dt in the coil. In this experiment, induction coils with different areas and numbers of turns are arranged in a cylindrical field coil through which alternating currents of various frequencies, amplitudes and signal forms flow. In the field coil, the currents generate the magnetic field N B = m0 · 2 · l L2 Vs where m0 = 4S · 10–7 (permeability) Am and I(t) is the time-dependent current level, N2 the number of turns and L2 the overall length of the coil. The curve over time U(t) of the voltages induced in the induction coils is recorded using the computer-based CASSY measuring system. This experiment explores how the voltage is dependent on the area and the number of turns of the induction coils, as well as on the frequency, amplitude and signal form of the exciter current. Induction in a conduction loop for a variable magnetic field P 3.4.3.1 117 Electromagnetic induction P 3.4.4 Eddy currents Electricity P 3.4.4.1 Waltenhofen’s pendulum: demonstration of an eddy-current brake P 3.4.4.2 Demonstrating the operating principle of an AC power meter Waltenhofen’s pendulum: demonstration of an eddy-current brake (P 3.4.4.1) When a metal disk is moved into a magnetic field, eddy currents are produced in the disk. The eddy currents generate a magnetic field which interacts with the inducing field to resist the motion of the disk. The energy of the eddy currents, which is liberated by the Joule effect, results from the mechanical work which must be performed to overcome the magnetic force. In the first experiment, the occurrence and suppression of eddy currents is demonstrated using Waltenhofen’s pendulum. The aluminum plate swings between the pole pieces of a strong electromagnet. As soon as the magnetic field is switched on, the pendulum is arrested when it enters the field. The pendulum oscillations of a slitted plate, on the other hand, are only slightly attenuated, as only weak eddy currents can form. The second experiment examines the workings of an alternating current meter. In principle, the AC meter functions much like an asynchronous motor with squirrel-cage rotor. A rotating aluminum disk is mounted in the air gap between the poles of two magnet systems. The current to be measured flows through the bottom magnet system, and the voltage to be measured is applied to the top magnet system. A moving magnetic field is formed which generates eddy currents in the aluminum disk. The moving magnetic field and the eddy currents produce an asynchronous angular momentum N1 “ P proportional to the electrical power P to be measured. The angular momentum accelerates the aluminum disk until it attains equilibrium with its counter-torque N2 “ C C: angular velocity of disk generated by an additional permanent magnet embedded in the turning disk. Consequently, at equilibrium N1 = N2 the angular velocity of the disk is proportional to the electrical power P. Cat. No. 560 34 342 07 560 32 562 34 Description Waltenhofen’s pendulum Clamp with knife-edge bearings Rotatable aluminium disc Large coil holder 1 1 1 1 1 1 2 1 562 11 562 15 562 18 U-core with yoke Coil with 1000 turns Extra-low voltage coil, 50 turns 1 2 1 1 562 13 560 31 521 545 521 39 Coil with 250 turns Pair of bored pole pieces DC Power supply 0...16 V, 5 A Variable extra-low voltage transformer 537 32 531 712 531 100 300 01 Rheostat 10 V Ammeter, AC, I ≤ 10 A, e.g. Multimeter METRAmax 3 Voltmeter, AC, U ≤ 25 V, e.g. Multimeter METRAmax 2 Stopclock I 30 s/15 min Stand base, V-shape, 28 cm 313 07 300 02 301 01 300 51 300 41 Stand base, V-shape, 20 cm Leybold multiclamp Stand rod, right-angled Stand rod, 25 cm 1 1 1 1 2 1 300 42 501 28 501 33 Stand rod, 47 cm Connecting lead, Ø = 2,5 mm2, 50 cm, black I Connecting lead, Ø = 2,5 mm2, 100 cm, black I 4 I AC meter model, complete (593 20) for P 3.4.4.2 118 P 3.4.4.2 1 1 1 1 P 3.4.4.1 1 9 Electricity Electromagnetic induction P 3.4.5 Transformer P 3.4.5.1 Voltage and current transformation with a transformer P 3.4.5.2 Voltage transformation with a transformer under load P 3.4.5.3 Recording the voltage and current of a transformer under load as a function of time Voltage transformation with a transformer (P 3.4.5.1) Cat. No. Description 562 801 521 35 537 32 531 100 531 100 524 010 524 011 524 200 459 23 514 72 514 73 500 414 500 444 Transformer for students experiments Variable extra low voltage transformer S Rheostat 10 V Ammeter, AC, I ≤ 3 A, e.g. Multimeter METRAmax 2 Voltmeter, AC, U ≤ 20 V, e.g. Multimeter METRAmax 2 Sensor CASSY Power CASSY CASSY Lab Acryllic glass screen on rod Shaker for iron filings Iron filings 250 g Connecting lead, 25 cm, black Connecting lead, 100 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Regardless of the physical design of the transformer, the voltage transformation of a transformer without load is determined by the ratio of the respective number of turns U2 N2 (when I2 = 0) = U1 N1 The current transformation in short-circuit operation is inversely proportional to the ratio of the number of turns N l2 = 2 (when U2 = 0) N1 l1 The behavior of the transformer under load, on the other hand, depends on its particular physical design. This fact can be demonstrated using the transformer for students’ experiments. The aim of the first experiment is to measure the voltage transformation of a transformer without load and the current transformation of a transformer in short-circuit mode. At the same time, the difference between an isolating transformer and an autotransformer is demonstrated. The second experiment examines the ratio between primary and secondary voltage in a “hard” and a “soft” transformer under load. In both cases, the lines of magnetic flux of the transformer are revealed using iron filings on a glass plate placed on top of the transformer. In the third experiment, the primary and secondary voltages and the primary and secondary currents of a transformer under load are recorded as time-dependent quantities using the computerbased CASSY measuring system. The CASSY software determines the phase relationships between the four quantities directly and additionally calculates the time-dependent power values of the primary and secondary circuits. 2 1 1 1 1 2 6 10 8 1 Recording the voltage and current of a transformer under load as a function of time (P 3.4.5.3 b) P 3.4.5.3 (b) 1 1 1 1 1 6 P 3.4.5.3 (a) P 3.4.5.2 P 3.4.5.1 1 119 Electromagnetic induction P 3.4.5 Transformer Electricity P 3.4.5.4 Power transmission of a transformer P 3.4.5.5 Experiments with high currents P 3.4.5.6 High-voltage experiments with a two-pronged lightning rod Power transmission of a transformer (P 3.4.5.4 a) As an alternative to the transformer for students’ experiments, the demountable transformer with a full range of coils is available which simply slide over the arms of the U-core, making them easily interchangeable. The experiments described for the transformer for students’ experiments (P 3.4.5.1-3) can of course be performed just as effectively using the demountable transformer, as well as a number of additional experiments. The first experiment examines the power transmission of a transformer. Here, the RMS values of the primary and secondary voltage and the primary and secondary current are measured on a variable load resistor 0 – 110 Ö using the computer-based CASSY measuring system. The phase shift between the voltage and current on the primary and secondary sides is determined at the same time. In the evaluation, the primary power P1, the secondary power P2 and the efficiency P J= 2 P1 are calculated and displayed in a graph as a function of the load resistance R. In the two other experiments, a transformer is assembled in which the primary side with 500 turns is connected directly to the mains voltage. In a melting ring with one turn or a welding coil with five turns on the secondary side, extremely high currents of up to 100 A can flow, sufficient to melt metals or spot-weld wires. Using a secondary coil with 23,000 turns, high voltages of up to 10 kV are generated, which can be used to produce electric arcs in horn-shaped spark electrodes. P 3.4.5.4 (b) P 3.4.5.4 (a) P 3.4.5.5 1 1 1 1 1 1 1 Cat. No. Description 562 11 562 12 562 13 562 17 562 21 562 19 562 31 562 20 562 32 521 35 537 34 524 011 524 010 524 200 500 414 500 444 U-core with yoke Clamping device Coil with 250 turns Coil with 23,000 turns Mains coil with 500 turns for 230 V Coil with 5 turns Set of 5 sheet metal strips Ring-shaped melting ladle Melting ring Variable extra low voltage transformer S Rheostat 100 V Power-CASSY Sensor-CASSY CASSY Lab Connecting lead, 25 cm, black Connecting lead, 100 cm, black additionally required: PC with Windows 95/NT or higher 1 1 2 1 1 2 1 1 1 1 2 1 2 8 1 1 1 1 5 1 120 P 3.4.5.6 1 1 1 1 Electricity Electromagnetic induction P 3.4.6 Measuring the earth’s magnetic field P 3.4.6.1 Measuring the earth’s magnetic field with a rotating induction coil (earth inductor) Measuring the earth’s magnetic field with a rotating induction coil (earth inductor) (P 3.4.6.1) Cat. No. 555 604 Description Pair of Helmholtz coils Experiment motor Control unit for experiment motor Sensor CASSY mV-box CASSY Lab Bench clamp with pin Connecting lead, Ø 2.5 mm2, 200 cm, red Connecting lead, Ø 2.5 mm2, 200 cm, blue additionally required: PC with Windows 95/NT or higher * additionally recommended 1 1* 1* 1 1 1 1* 1 1 1 347 35 347 36 524 010 524 040 524 200 301 05 501 35 501 36 When a circular induction loop with N turns and a radius R rotates in a homogeneous magnetic field B around its diameter as its axis, it is permeated by a magnetic flux of F(t) = N · S · R2 · n(t) · B n(t) = normal vector of a rotating loop If the angular velocity v is constant, we can say that F(t) = N · S · R2 · Bb · cos vt Where Bb is the effective component of the magnetic field perpendicular to the axis of rotation. We can determine the magnetic field from the amplitude of the induced voltage U0 = N · S · R2 · Bb · v To achieve the maximum measuring accuracy, we need to use the largest possible coil. In this experiment the voltage U(t) induced in the earth’s magnetic field for various axes of rotation is measured using the computer-based CASSY measuring system. The amplitude and frequency of the recorded signals and the respective active component Bb are used to calculate the earth’s magnetic field. The aim of the evaluation is to determine the total value, the horizontal component and the angle of inclination of the earth’s magnetic field. P 3.4.6.1 121 Electrical machines P 3.5.1 Basic experiments on electrical machines P 3.5.1.1 Investigating the interactions of forces of rotors and stators P 3.5.1.2 Simple induction experiments with electromagnetic rotors and stators Electricity Simple induction experiments with electromagnetic rotors and stators (P 3.5.1.2) The term “electrical machines” is used to refer to both motors and generators. Both devices consist of a stationary stator and a rotating armature or rotor. The function of the motors is due to the interaction of the forces arising through the presence of a current-carrying conductor in a magnetic field, and that of the generators is based on induction in a conductor loop moving within a magnetic field. The action of forces between the magnetic field and the conductor is demonstrated in the first experiment using permanent and electromagnetic rotors and stators. A magnet model is used to represent the magnetic fields. The object of the second experiment is to carry out qualitative measurements on electromagnetic induction in electromagnetic rotors and stators. Cat. No. 563 480 727 81 560 61 521 48 531 100 500 422 501 45 501 46 Description Electrical motor and generator models, basic set Basic machine unit Cubical magnet model AC/DC power supply 0....12 V, 230 V/ 50 Hz Voltmeter, DC, |U | ≤ 3 V, e. g. Multimeter METRAmax 2 Connection lead, 50 cm, blue Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 1 122 P 3.5.1.2 1 1 1 P 3.5.1.1 Electricity Electrical machines P 3.5.2 Electric generators P 3.5.2.1 Generating AC voltage with a revolving-field generator (dynamo) and a revolvingarmature generator P 3.5.2.2 Generating DC voltage with a revolving-armature generator P 3.5.2.3 Generating AC voltage with a power-plant generator (generator with electromagnetic revolving field) P 3.5.2.4 Generating voltage with an ACDC generator (generator with electromagnetic revolving armature) P 3.5.2.5 Generating voltage with selfexcited generators Generating AC voltage with a revolving-field generator (dynamo) and a revolving-armature generator (P 3.5.2.1) Cat. No. Description 563 480 563 23 727 81 563 302 726 19 301 300 521 48 537 36 531 100 531 291 575 211 575 24 313 07 Electrical motor and generator models, basic set Three-pole rotor Basic machine unit Hand cranked gear Panel frame, SL 85 Demonstration-experiment frame Power supply, DC (stabilized), e.g. AC/DC power supply 0....12 V Rheostat 1000 V Multimeter, AC/DC, e.g. Multimeter METRAmax 2 Digital-analog multimeter METRAHit 25 S Two-channel oscilloscope 303 Screened cable BNC/4 mm Stopclock I 30 s/15 min 1 1 1 1* 1 1* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1* 1* 1* 1* 1 1 2 2 1 1 1 1 1 2 1 2 1 1 1 2 1 2 2 2 1 500 422 Connection lead, 50 cm, blue 501 45 501 46 Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue * additionally recommended Electric generators exploit the principle of electromagnetic induction discovered by Faraday to convert mechanical into electrical energy. We distinguish between revolving-armature generators (excitation of the magnetic field in the stator, induction in the rotor) and revolving-field generators (excitation of the magnetic field in the rotor, induction in the stator). Both types of generators are assembled in the first experiment using permanent magnets. The induced AC voltage U is measured as a function of the speed f of the rotor. Also, the electrical power P produced at a fixed speed is determined as a function of the load resistance R. The second experiment demonstrates the use of a commutator to rectify the AC voltage generated in the rotor of a rotating-armature generator. The number of rectified half-waves per rotor revolution increases when the two-pole rotor is replaced with a threepole rotor. The third and fourth experiments investigate generators which use electromagnets instead of permanent magnets. Here, the induced voltage depends on the excitation current of the magnetic field. The excitation current can be used to vary the generated power without changing the speed of the rotor or the frequency of the AC voltage. This principle is used in power-plant generators. In the AC /DC generator, the voltage can also be tapped via the commutator in rectified form. The final experiment examines generators in which the magnetic field of the stator is amplified by the generator current by means of self-excitation. The stator and rotor windings are conductively connected with each other. We distinguish between serieswound generators, in which the rotor, stator and load are all connected in series, and shunt-wound generators, in which the stator and the load are connected in parallel to the rotor. P 3.5.2.3-4(b) P 3.5.2.3-4(a) P 3.5.2.2(b) P 3.5.2.2(a) P 3.5.2.5(a) P 3.5.2.1(b) P 3.5.2.1(a) P 3.5.2.5(b) 123 Electrical machines P 3.5.3 Electric motors Electricity P 3.5.3.1 Investigating a DC motor with two-pole rotor P 3.5.3.2 Investigating a DC motor with three-pole rotor P 3.5.3.3 Investigating a series-wound and shunt-wound universal motor P 3.5.3.4 Principle of an AC synchronous motor Investigating a DC motor with two-pole rotor (P 3.5.3.1) Electric motors exploit the force acting on current-carrying conductors in magnetic fields to convert electrical energy into mechanical energy. We distinguish between asynchronous motors, in which the rotor is supplied with AC or DC voltage via a commutator, and synchronous motors, which have no commutator, and whose frequencies are synchronized with the frequency of the applied voltage. The first experiment investigates the basic function of an electric motor with commutator. The motor is assembled using a permanent magnet as stator and a two-pole rotor. The polarity of the rotor current determines the direction in which the rotor turns. This experiment measures the relationship between the applied voltage U and the no-load speed f0 as well as, at a fixed voltage, the current I consumed as a function of the load-dependent speed f. The use of the three-pole rotor is the object of the second experiment. The rotor starts turning automatically, as an angular momentum (torque) acts on the rotor for any position in the magnetic field. To record the torque curve M(f), the speed f of the rotor is recorded as a function of a counter-torque M. In addition, the mechanical power produced is compared with the electrical power consumed. The third experiment takes a look at the so-called universal motor, in which the stator and rotor fields are electrically excited. The stator and rotor coils are connected in series (“serieswound”) or in parallel (“shunt-wound”) to a common voltage source. This motor can be driven both with DC and AC voltage, as the torque acting on the rotor remains unchanged when the polarity is reversed. The torque curve M(f) is recorded for both circuits. The experiment shows that the speed of the shuntwound motor is less dependent on the load than that of the series-wound motor. In the final experiment, the rotor coil of the AC synchronous motor is synchronized with the frequency of the applied voltage using a hand crank, so that the rotor subsequently continues running by itself. P 3.5.3.2(b) P 3.5.3.3(b) P 3.5.3.2(a) P 3.5.3.3(a) Cat. No. Description 563 480 563 23 727 81 563 302 726 19 301 300 521 35 531 100 531 100 451 281 314 161 314 151 309 50 576 71 579 13 579 06 505 18 666 470 300 41 501 45 501 46 Electrical motor and generator models, basic set Three-pole rotor Basic machine unit Hand cranked gear Panel frame, SL 85 Demonstration-experiment frame 1 1 1 1 1 1 1 1 1* 1 1 1* 1 P 3.5.3.4(a) 1 1 1 1 1 1 1 1 1 1 2 P 3.5.3.1(b) P 3.5.3.1(a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Power supply, AC/DC, U ≤ 20 V, e. g. Variable low voltage transformer S 1 Ammeter, AC/DC, I ≤ 3 A, e. g. Multimeter METRAmax 2 Voltmeter, AC/DC, U ≤ 20 V, e. g. Multimeter METRAmax 2 Stroboscope, 230 V, 50 Hz Precision dynamometer, 5.0 N Precision dynamometer, 2.0 N Demonstration cord, 20 m Plug-in board section STE toggle switch, single pole STE lamp holder E 10, top Incandescent lamp E 10; 24.0 V/3.0 W CPS-holder with bosshead, height adjustable Stand rod, 25 cm Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue * additionally recommended 1 2 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 2 2 1 1 2 2 2 124 P 3.5.3.4(b) 1 1 1 1 1 1 1 1 1 1 Electricity Electrical machines P 3.5.4 Three-phase machines P 3.5.4.1 Experiments with a three-phase revolving-armature generator P 3.5.4.2 Experiments with a three-phase revolving-field generator P 3.5.4.3 Comparing star and delta connections on a three-phase generator P 3.5.4.4 Assembling synchronous and asynchronous three-phase motors Experiments with a three-phase revolving-armature generator (P 3.5.4.1) Cat. No. Description 563 480 563 481 563 12 727 81 563 302 726 50 579 06 505 14 501 48 521 48 521 29 531 100 575 211 575 24 313 07 726 19 301 300 500 414 501 451 Electric motor and generator models, basic set Electric motor and generator models, supplementary set Short-circuit rotor Basic machine unit Hand cranked gear Plug-in board 297 x 300 mm STE lamp holder, E10, top Set of 10 lamps E 10; 6.0 V/3.0 W Set of 10 bridging plugs AC/DC-power supply 0....12 V, 230 V/50 Hz 3-phase extra-low voltage transformer Multimeter, AC/DC, e.g. METRAmax 2 Two-channel oscilloscope 303 Screened cable BNC/4 mm Stopclock I, 30s/15min Panel frame, SL 85 Demonstration-experiment frame Connecting lead, black, 25 cm Pair of cables, 50 cm, black * additionally recommended 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1* 2* 1* 1 1 3 1* 2* 1* 3 1* 2* 1* 1 1 3 3 3 4 4 6 3 1* 2* 1* 1 1 3 6 3 2 1 2 2 1 1 1 1 3 2 In the real world, power is supplied mainly through the generation of three-phase AC, usually referred to simply as “threephase current”. Consequently, three-phase generators and motors are extremely significant in actual practice. In principle, their function is analogous to that of AC machines. As with AC machines, we differentiate between revolving-armature and revolving-field generators, and between asynchronous and synchronous motors. The simplest configuration for generating three-phase current, a revolving-armature generator which rotates in a permanent magnetic field, is assembled in the first experiment using a threepole rotor. The second experiment examines the more common revolving-field generator, in which the magnetic field of the rotor in the stator coils is induced by phase-shifted AC voltages. In both cases, instruments for measuring current and voltage, and for observing the phase shift for a slowly turning rotor, are connected between two taps. For faster rotor speeds, the phase shift is measured using an oscilloscope. In the third experiment, loads are connected to the three-phase generator in star and delta configuration. In the star configuration, the relationship Uaa = öä 3 Ua0 is verified for the voltages Uaa between any two outer conductors as well as Ua0 between the outer and neutral conductors. For the currents I1 flowing to the loads and the currents I2 flowing through the generator coils in delta configuration, the result is I1 = öä 3. I2 The final experiment examines the behavior of asynchronous and synchronous machines when the direction of rotation is reversed. P 3.5.4.3 (b) P 3.5.4.4 (b) P 3.5.4.2 (b) P 3.5.4.2 (a) P 3.5.4.3 (a) P 3.5.4.4 (a) P 3.5.4.1 (b) P 3.5.4.1 (a) 125 DC and AC circuits P 3.6.1 Circuit with capacitor Electricity P 3.6.1.1 Charging and discharging a capacitor when switching DC on and off P 3.6.1.2 Determining the capacitive reactance of a capacitor in an AC circuit Charging and discharging a capacitor when switching DC on and off (P 3.6.1.1) To investigate the behavior of capacitors in DC and AC circuits, the voltage UC at a capacitor is measured using a two-channel oscilloscope, and the current IC through the capacitor is additionally calculated from the voltage drop across a resistor R connected in series. The circuits for conducting these measurements are assembled on a plug-in board using the STE plug-in system. A function generator is used as a voltage source with variable amplitude and variable frequency. In the first experiment, the function generator generates periodic square-wave signals which simulate switching a DC voltage on and off. The square-wave signals are displayed on channel I of the oscilloscope, and the capacitor voltage or capacitor current is displayed on oscilloscope channel II. The aim of the experiment is to determine the time constant t=R·C for various capacitances C from the exponential curve of the respective charging or discharge current IC. In the second experiment, an AC voltage with the amplitude U0 and the frequency f is applied to a capacitor. The voltage UC(t) and the current IC(t) are displayed simultaneously on the oscilloscope. The experiment shows that in this circuit the current leads the voltage by 90°. In addition, the proportionality between the voltage amplitude U0 and the current amplitude I0 is confirmed, and for the proportionality constant ZC = U0 I0 Cat . No. 576 74 577 19 577 20 577 40 577 44 577 48 578 15 522 621 Description Plug-in board A4 STE resistor 001 V, 2 W STE resistor 010 V, 2 W STE resistor 470 V, 2 W STE resistor 0.1 kV, 2 W STE resistor 2.2 kV, 2 W STE capacitor 1 µF, 100 V Function generator S 12, 0.1 Hz to 20 kHz 1 1 1 1 3 1 3 1 575 211 575 24 501 46 Two-channel oscilloscope 303 Screened cable BNC/4 mm Pair of cables, 1 m, red and blue 1 2 1 the relationship ZC = – is revealed. 1 2öf · C Schematic circuit diagram 126 P 3.6.1.2 1 1 1 1 2 1 P 3.6.1.1 Electricity DC and AC circuits P 3.6.2 Circuit with coil P 3.6.2.1 Measuring the current in a coil when switching DC on and off P 3.6.2.2 Determining the inductive reactance of a coil in an AC circuit Measuring the current in a coil when switching DC on and off (P 3.6.2.1) Cat. No. 576 74 577 19 577 20 577 24 577 28 590 84 501 48 522 621 Description Plug-in board A4 STE resistor 01 V, 2 W STE resistor 10 V, 2 W STE resistor 22 V, 2 W STE resistor 47 V, 2 W Coil with 1000 turns Set of 10 bridging plugs Function generator S 12, 0.1 Hz to 20 kHz 1 1 1 1 1 1 2 1 1 1 2 1 1 575 211 575 24 501 46 Two-channel oscilloscope 303 Screened cable BNC/4 mm Pair of cables, 1 m, red and blue 1 2 1 1 2 1 To investigate the behavior of coils in DC and AC circuits, the voltage UL at a coil is measured using a two-channel oscilloscope, and the current IL through the coil is additionally calculated from the voltage drop across a resistor R connected in series. The circuits for conducting these measurements are assembled on a plug-in board using the STE plug-in system for electricity/electronics. A function generator is used as a voltage source with variable amplitude and variable frequency. In the first experiment, the function generator generates periodic square-wave signals which simulate switching a DC voltage on and off. The square-wave signals are displayed on channel I of the oscilloscope, and the coil voltage or coil current is displayed on oscilloscope channel II. The aim of the experiment is to determine the time constant t= L R P 3.6.2.2 P 3.6.2.1 for different inductances L from the exponential curve of the coil voltage UL. In the second experiment, an AC voltage with the amplitude U0 and the frequency f is applied to a coil. The voltage UL(t) and the current IL(t) are displayed simultaneously on the oscilloscope. The experiment shows that in this circuit the current lags behind the voltage by 90°. In addition, the proportionality between the voltage amplitude U0 and the current amplitude I0 is confirmed, and, for the proportionality constant ZL = U0 I0 the relationship ZL = 2π f · L Schematic circuit diagram is revealed. 127 DC and AC circuits P 3.6.3 Impedance Electricity P 3.6.3.1 Determining the impedance in circuits with capacitors and ohmic resistors P 3.6.3.2 Determining the impedance in circuits with coils and ohmic resistors P 3.6.3.3 Determining the impedance in circuits with capacitors and coils Determining the impedance in circuits with capacitors and ohmic resistors (P 3.6.3.1) The current I(t) and the voltage U(t) in an AC circuit are measured as time-dependent quantities using a dual-channel oscilloscope. A function generator is used as a voltage source with variable amplitude U0 and variable frequency f. The measured quantities are then used to determine the absolute value of the total impedance U Z= 0 I0 and the phase shift f between the current and the voltage. A resistor R is combined with a capacitor C in the first experiment, and an inductor L in the second experiment. These experiments confirm the relationship Z Zs = öR2 + Z2l and tan f s = l R 1 with Zl = – resp. Zl = 2öf · L 2öf · C for series connection and 1 ZP = Cat. No. 576 74 577 19 577 20 577 32 577 56 578 12 578 15 578 16 578 31 590 83 590 84 522 621 Description Plug-in board A4 STE resistor 001 V, 2 W STE resistor 010 V, 2 W STE resistor 100 V, 2 W STE resistor 10 kV, 0.5 W STE capacitor 10 µF, 100 V STE capacitor 01 µF, 100 V STE capacitor 4.7 µF, 63 V STE capacitor 0.1µF, 100 V Coil with 500 turns Coil with 1000 turns Function generator S 12, 0.1 Hz to 20 kHz 1 1 P 3.6.3.2 1 1 1 1 1 1 1 1 2 1 P 3.6.3.1 1 1 1 1 1 1 1 1 1 575 211 575 24 501 46 Two-channel oscilloscope 303 Screened cable BNC/4 mm Pair of cables, 1 m, red and blue 1 2 1 ö 1 R2 + 1 Zl2 and tanfp = R Zl for parallel connection. The third experiment examines the oscillator circuit as the series and parallel connection of capacitance and inductance. The total impedance of the series circuit 1 Zs = 2öf · L – 2öf · C disappears at the resonance frequency fr = 1 2ö · i.e. at a given current I the total voltage U at the capacitor and the coil is zero, because the individual voltages UC and UL are equal and opposite. For parallel connection, we can say 1 ZP = 1 2öf · L – 2öf · C. ßLC , At the resonance frequency, the impedance of this circuit is infinitely great; in other words, at a given voltage U the total current I in the incumingine is zero, as the two individual currents IC and IL are equal and opposed. 128 P 3.6.3.3 1 1 1 1 1 1 2 1 Electricity DC and AC circuits P 3.6.4 Measuring-bridge circuits P 3.6.4.1 Determining capacitive reactance with a Wien measuring bridge P 3.6.4.2 Determining inductive reactance with a Maxwell measuring bridge Determining capacitive reactance with a Wien measuring bridge (P 3.6.4.1) Cat. No. 576 74 577 01 577 93 578 15 578 16 579 29 590 83 590 84 501 48 522 621 Description Plug-in board A4 STE resistor 100 V, 0.5 W STE 10-turn potentiometer 1 kV STE capacitor 1 µF, 100 V STE capacitor 4.7 µF, 63 V Earphone, 2 kV Coil with 500 turns Coil with 1000 turns Set of 10 bridging plugs 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 The Wheatstone measuring bridge is one of the most effective means of measuring ohmic resistance in DC and AC circuits. Capacitive and inductive reactance can also be determined by means of analogous circuits. These measuring bridges consist of four passive bridge arms which are connected to form a rectangle, an indicator arm with a null indicator and a supply arm with the voltage source. Inserting variable elements in the bridge arm compensates the current in the indicator arm to zero. Then, for the component resistance values, the fundamental compensation condition Z Z1 = Z2 · 3 , Z4 applies, from which the measurement quantity Z1 is calculated. The first experiment investigates the principle of a Wien measuring bridge for measuring a capacitive reactance Z1. In this configuration, Z2 is a fixed capacitive reactance, Z3 is a fixed ohmic resistance and Z4 is a variable ohmic resistance. For zero compensation, the following applies regardless of the frequency of the AC voltage: 1 1 R3 = · C1 C2 R4 An oscilloscope or an earphone can alternatively be used as a zero indicator. In the second experiment, a Maxwell measuring bridge is assembled to determine the inductive reactance Z1. As the resistive component of Z1 is also to be compensated, this circuit is somewhat more complicated. Here, Z2 is a variable ohmic resistance, Z3 is a fixed ohmic resistance and Z4 is a parallel connection consisting of a capacitive reactance and a variable ohmic resistor. For the purely inductive component, the following applies with respect to zero compensation: 2πf · L1 = R2 · R3 · 2πf · C4 f: AC voltage frequency. 1 1 Function generator S 12, 0.1 Hz to 20 kHz Two-channel oscilloscope 303 Screened cable BNC/4 mm Pair of cables, 50 cm, red and blue 1 1 1 1 P 3.6.4.2 (a) 1 1 1 P 3.6.4.1 (b) P 3.6.4.1 (a) 575 211 575 24 501 45 1 1 P 3.6.4.1 P 3.6.4.2 P 3.6.4.2 (b) 1 1 1 1 129 DC and AC circuits P 3.6.5 Measuring AC voltages and currents P 3.6.5.1 Frequency response and curve form factor of a multimeter Electricity Frequency response and curve form factor of a multimeter (P 3.6.5.1) When measuring voltages and currents in AC circuits at higher frequencies, the indicator of the meter no longer responds in proportion to the voltage or current amplitude. The ratio of the reading value to the true value as a function of frequency is referred to as the “frequency response”. When measuring AC voltages or currents in which the shape of the signal deviates from the sinusoidal oscillation, a further problem occurs. Depending on the signal form, the meter will display different current and voltage values at the same frequency and amplitude. This phenomenon is described by the wave form factor. This experiment determines the frequency response and wave form factor of a multimeter. Signals of a fixed amplitude and varying frequencies are generated using a function generator and measured using the multimeter. Cat. No. 531 100 536 131 522 621 Description Multimeter METRAmax 2 Measuring resistor 100 V, 4 W Function generator S 12, 0.1 Hz to 20 kHz 575 211 575 24 500 424 Two-channel oscilloscope 303 Screened cable BNC/4 mm Connection lead, 50 cm, black * additionally recommended 130 P 3.6.5.1 2 1 1 1* 1* 5 Electricity DC and AC circuits P 3.6.6 Electrical work and power P 3.6.6.1 Determining the heating power of an ohmic load in an AC circuit as a function of the applied voltage P 3.6.6.2 Measuring the electrical work of an immersion heater using an AC power meter Measuring the electrical work of an immersion heater using an AC power meter (P 3.6.6.2) Cat. No. 590 50 384 52 560 331 301 339 303 25 521 35 531 100 531 100 531 712 313 07 382 34 590 06 500 624 501 23 501 28 Description Lid with heater Aluminium calorimeter Alternating current meter Pair of stand feet Immersion heater Voltage source, AC 0...12 V, 6 A P 3.6.6.2 P 3.6.6.1 The relationship between the power P at an ohmic resistance R and the applied voltage U can be expressed with the relationship P= U2 . R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 2 Variable extra low voltage transformer S Voltmeter, AC, U ≤ 12 V, e. g. Multimeter METRAmax 2 Voltmeter, AC, U ≤ 230 V, e. g. Multimeter METRAmax 2 Ammeter, AC, I ≤ 6 A, e. g. Multimeter METRAmax 3 Stopclock I, 30 s/15 min Thermometer, -10 to +110 °C Plastic beaker, 1000 ml Safety connection lead, 50 cm, black Connecting lead, Ø 2.5 mm2, 25 cm, black Connecting lead, Ø 2,5 mm2, 50 cm, blue The same applies for AC voltage when P is the power averaged over time and U is replaced by the RMS value U Urms = 0 ö2 U0: amplitude of AC voltage. The relationship P=U·I can also be applied to ohmic resistors in AC circuits when the direct current I is replaced by the RMS value of the AC I Irms = 0 ö2 I0: amplitude of AC. In the first experiment, the electrical power of an immersion heater for extra-low voltage is determined from the Joule heat emitted per unit of time and compared with the applied voltage Urms. This experiment confirms the relationship P“U2 . rms In the second experiment, an AC power meter is used to determine the electrical work W which must be performed to produce one liter of hot water using an immersion heater. For comparison purposes, the voltage Urms, the current Irms and the heating time t are measured and the relationship W = Urms · Irms · t is verified. 131 DC and AC circuits P 3.6.6 Electrical work and power Electricity P 3.6.6.3 Quantitative comparison of DC power and AC power using an incandescent lamp P 3.6.6.4 Determining the crest factors of various AC signal forms P 3.6.6.5 Determining the active and reactive power in AC circuits Determining the active and reactive power in AC circuits (P 3.6.6.5) The electrical power of a time-dependent voltage U(t) at any load resisance is also a function of time: P(t) = U(t) · l(t) I(t): time-dependent current through the load resistor. Thus, for periodic currents and voltages, we generally consider the power averaged over one period T. This quantity is often referred to as the active power PW. It can be measured electronically for any DC or AC voltages using the joule and wattmeter. In the first experiment, two identical incandescent light bulbs are operated with the same electrical power. One bulb is operated with DC voltage, the other with AC voltage. The equality of the power values is determined directly using the joule and wattmeter, and additionally by comparing the lamp brightness levels. This equality is reached when the DC voltage equals the RMS value of the AC voltage. The object of the second experiment is to determine the crest factors, i. e. the quotients of the amplitude U0 and the RMS value Urms for different AC voltage signal forms generated using a function generator by experimental means. The amplitude is measured using an oscilloscope. The RMS value is calculated from the power P measured at an ohmic resistor R using the joule and wattmeter according to the formula Ueff = öP · R . The third experiment measures the current Irms through a given load and the active power PW for a fixed AC voltage Urms. To verify the relationship PW = Ur ms · Ir ms · cos f the phase shift f between the voltage and the current is additionally determined using an oscilloscope. This experiment also shows that the active power for a purely inductive or capacitive load is zero, because the phase shift is f = 90°. The apparent power Ps = Urms · Irms is also referred to as reactive power in this case. 132 P 3.6.6.3 P 3.6.6.4 1 1 1 1 1 2 3 Cat. No. 531 83 505 14 576 71 579 06 522 56 522 61 536 101 537 35 517 021 562 11 562 12 562 15 521 48 521 35 531 100 531 100 575 211 575 24 575 35 504 45 500 421 501 45 501 46 Description Joule and Wattmeter Set of 10 lamps E 10; 6.0 V/3.0 W Plug-in board section STE lamp holder E 10, top Function generator P, 100 mHz to 100 kHz AC/DC amplifier, 30 W Measuring resistor 1 V, 4 W Rheostat 330 V Capacitor, 40 µF, on plate U-core with yoke Clamping device Coil with 1 000 turns Voltage source, AC/DC, 0–12 V, 3 A, e. g. AC/DC power supply 0....12 V, 230 V/50 Hz Voltage source, AC, 0–20 V, 1 A, e.g. Variable extra low voltage transformer S Voltmeter, AC/DC, U ≤ 12 V, e.g. Multimeter METRAmax 2 Voltmeter, AC, U ≤ 20 V, e.g. Multimeter METRAmax 2 Two-channel oscilloscope 303 Screened cable BNC/4 mm BNC/4 mm adapter, 2-pole Single-pole cut-out switch Connection lead, 50 cm, red Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue 1 2 2 2 1 1 1 1 1 2 2 1 1 2 2 3 2 P 3.6.6.5 1 1 1 1 1 1 Electricity DC and AC circuits P 3.6.7 Electromechanical devices P 3.6.7.1 Demonstration of the function of a bell P 3.6.7.2 Demonstration of the function of a relay Demonstration of the function of a relay (P 3.6.7.2) Cat. No. Description 561 071 301 339 579 10 579 13 579 30 576 71 579 06 505 13 521 210 Bell/relay set, complete Pair of stand feet STE key switch n.o., single pole STE toggle switch, single pole STE adjustable contact Plug-in board section STE lamp holder E 10, top Lamp with socket, E 10; 6.0 V/5.0 W Transformer, 6 V AC, 12 V AC / 30 W Connection lead, 100 cm, black 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 5 2 2 2 1 7 500 444 In the first experiment, an electric bell is assembled using a hammer interrupter (Wagner interrupter). The hammer interrupter consists of an electromagnet and an oscillating armature. In the resting state, the oscillating armature touches a contact, thus switching the electromagnet on. The electromagnet attracts the oscillating armature, which strikes a bell. At the same time, this action interrupts the circuit, and the oscillating armature returns to the resting position. The second experiment demonstrates how a relay functions. A control circuit operates an electromagnet which attracts the armature of the relay. When the electromagnet is switched off, the armature returns to the resting position. When the armature touches a contact, a second circuit is closed, which e.g. supplies power to a lamp. When the contact is configured so that the armature touches it in the resting state, we call this a break contact; the opposite case is termed a make contact. Function principle of a relay (P 3.6.7.2) P 3.6.7.2 (b) P 3.6.7.2 (a) P 3.6.7.1 133 Electromagnetic oscillations and waves P 3.7.1 Electromagnetic oscillator circuit P 3.7.1.1 P 3.7.1.2 Free electromagnetic oscillations De-damping of electromagnetic oscillations through inductive three-point coupling after Hartley Electricity Free electromagnetic oscillations (P 3.7.1.1 a) Electromagnetic oscillation usually occurs in a frequency range in which the individual oscillations cannot be seen by the naked eye. However, this is not the case in an oscillator circuit consisting of a high-capacity capacitor (C = 40 mF) and a high-inductance coil (L = 500 H). Here, the oscillation period is about 1 s, so that the voltage and current oscillations can be observed directly on a pointer instrument or Yt recorder. The first experiment investigates the phenomenon of free electromagnetic oscillations. The damping is so low that multiple oscillation periods can be observed and their duration measured with e. g. a stopclock. In the process, the deviations between the observed oscillation periods and those calculated using Thomson’s equation T = 2ö · öL · C are observed. These deviations can be explained by the currentdependency of the inductance, as the permeability of the iron core of the coil depends on the magnetic field strength. In the second experiment, an oscillator circuit after Hartley is used to “de-damp” the electromagnetic oscillations in the circuit, or in other words to compensate the ohmic energy losses in a feedback loop by supplying energy externally. Oscillator circuits of this type are essential components in transmitter and receiver circuits used in radio and television technology. A coil with center tap is used, in which the connection points are connected with the emitter, base and collector of a transistor via AC. The base current controls the collector current synchronously with the oscillation to compensate for energy losses. P 3.7.1.2 (b) 1 1 2 1 1 1 1 1 1 1 1 1 3 2 P 3.7.1.2 (a) Cat. No. Description 517 011 517 021 301 339 576 74 576 86 503 11 577 01 577 10 578 76 579 13 501 48 521 45 531 94 575 713 Coil with high inductivity, on plate Capacitor, 40 µF, on plate Pair of stand feet Plug-in board A4 STE mono cell holder Set of 20 batteries 1.5 V (type MONO) STE resistor 100 V, 0.5 W STE resistor 100 kV, 0.5 W STE transistor BC 140, NPN, emitter bottom STE toggle switch, single pole Set of 10 bridging plugs DC power supply 0....+/- 15 V AV-meter Yt-recorder, two channel Sensor-CASSY CASSY Lab Stopclock I, 30 s/15 min Connection lead, 50 cm, black Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 524 010 524 200 313 07 500 424 501 46 1 1 3 3 2 1 2 3 3 1 1 134 P 3.7.1.2 (c) 1 1 2 1 1 1 1 1 1 1 1 1 1 P 3.7.1.1 (b) P 3.7.1.1 (c) P 3.7.1.1 (a) Electricity Electromagnetic oscillations and waves P 3.7.2 Decimeter waves P 3.7.2.1 Radiation characteristic and polarization of decimeter waves P 3.7.2.2 Amplitude modulation of decimeter waves P 3.7.2.4 Estimating the dielectric constant of water in the decimeter-wave range Estimating the dielectric constant of water in the decimeter-wave range (P 3.7.2.4) Cat. No. 587 55 Description Decimeter wave transmitter 1 1 1 587 54 587 08 522 56 522 61 575 24 531 51 300 11 501 33 501 38 Set of dipoles in water tank Broad-band speaker Function generator P, 100 mHz to 100 kHz AC/DC-amplifier 30 W Screened cable BNC/4 mm Multimeter MA 1H Saddle base Connecting lead, Ø 2.5 mm2, 100 cm, black Connecting lead, Ø 2.5 mm2, 200 cm, black 2 1 2 3 4 1 1 1 1 1 1 It is possible to excite electromagnetic oscillations in a straight conductor in a manner analogous to an oscillator circuit. An oscillator of this type emits electromagnetic waves, and their radiated intensity is greatest when the conductor length is equivalent to exactly one half the wavelength (we call this a Ö/2 dipole). Experiments on this topic are particularly successful with wavelengths in the decimeter range. We can best demonstrate the existence of such decimeter waves using a second dipole which also has the length Ö/2, and from which the voltage is applied to an incandescent lamp or (via a high-frequency rectifier) to a measuring instrument. The first experiment investigates the radiation characteristic of a Ö/2 dipole for decimeter waves. Here, the receiver is aligned parallel to the transmitter and moved around the transmitter. In a second step, the receiver is rotated with respect to the transmitter in order to demonstrate the polarization of the emitted decimeter waves. The next experiment deal with the transmission of audiofrequency signals using amplitude-modulated decimeter waves. In amplitude modulation a decimeter-wave signal E(t) = E0 · cos(2S · f · t) is modulated through superposing of an audio-frequency signal u(t) in the form EAM(t) = E0 · (1 + kAM · u(t) ) · cos(2S · f · t) kAM: coupling coefficient The last experiment demonstrates the dielectric nature of water. In water, decimeter waves of the same frequency propagate with a shorter wavelength than in air. Therefore, a receiver dipole tuned for reception of the wavelength in air is no longer adequately tuned when placed in water. P 3.7.2.2 P 3.7.2.4 P 3.7.2.1 135 Electromagnetic oscillations and waves P 3.7.3 Propagation of decimeter waves along lines P 3.7.3.1 Determining the current and voltage maxima on a Lecher line P 3.7.3.2 Investigating the current and voltage on a Lecher line with loop dipole Electricity Determining the current and voltage maxima on a Lecher line (P 3.7.3.1) E. Lecher (1890) was the first to suggest using two parallel wires for directional transmission of electromagnetic waves. Using such Lecher lines, as they are known today, electromagnetic waves can be transmitted to any point in space. They are measured along the line as a voltage U(x,t) propagating as a wave, or as a current I(x,t). In the first experiment, a Lecher line open at the wire ends and a shorted Lecher line are investigated. The waves are reflected at the ends of the wires, so that standing waves are formed. The current is zero at the open end, while the voltage is zero at the shorted end. The current and voltage are shifted by Ö/4 with respect to each other, i. e. the wave antinodes of the voltage coincide with the wave nodes of the current. The voltage maxima are located using a probe with an attached incandescent lamp. An induction loop with connected incandescent lamp is used to detect the current maxima. The wavelength Ö is determined from from the intervals d between the current maxima or voltage maxima. We can say Ö d= 2 In the second experiment, a transmitting dipole (Ö/2 folded dipole) is attached to the end of the Lecher line. Subsequently, it is no longer possible to detect any voltage or current maxima on the Lecher line itself. A current maximum is detectable in the middle of the dipole, and voltage maxima at the dipole ends. Cat. No. Description 587 55 Decimeter wave transmitter 587 56 311 77 300 11 Lecher system with accessories Steel tape measure, 2 m Saddle base Current and voltage maxima on a Lecher line 136 P 3.7.3.1-2 1 1 1 3 Electricity Electromagnetic oscillations and waves P 3.7.4 Microwaves P 3.7.4.1 P 3.7.4.2 P 3.7.4.3 P 3.7.4.4 P 3.7.4.5 P 3.7.4.6 Field orientation and polarization of microwaves in front of a horn antenna Absorption of microwaves Determining the wavelength of standing microwaves Diffraction of microwaves Refraction of microwaves Investigating total reflection with microwaves Diffraction of microwaves at a double slit (P 3.7.4.4) Cat. No. 737 01 737 020 Description Gunn oscillator Gunn power supply 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1* 1 1 1 1 1 1 1 1 309 06 578 Stand rod 245 mm, with thread 737 21 737 27 737 275 737 35 737 390 Large horn antenna Physics microwave accessories I Physics microwave accessories II E-field probe Set of absorbers Voltmeter, DC, U ≤ 10 V, e.g. Multimeter METRAmax2 Stand base, V-shape, 20 cm Saddle base BNC cable, 2 m long Pair of cables, 1 m, black *additionally recommended 1 1 1* 1 1 1* 1 1* 1 1* 1 1* 531 100 300 02 300 11 501 022 501 461 1 1 1 1 1 1 1 2 2 1 2 2 1 3 2 1 4 2 1 2 2 1 2 2 1 Microwaves are electromagnetic waves in the wavelength range between 0.1 mm and 100 mm. They are generated e.g. in a cavity resonator, whereby the frequency is determined by the volume of the cavity resonator. An E-field probe is used to detect the microwaves; this device measures the parallel component of the electric field. The output signal of the probe is proportional to the square of the field strength, and thus to the intensity. The first experiment investigates the orientation and polarization of the microwave field in front of a radiating horn antenna. Here, the field in front of the horn antenna is measured point by point in both the longitudinal and transverse directions using the Efield probe. To determine the polarization, a rotating polarization grating made of thin metal strips is used; in this apparatus, the electric field can only form perpendicular to the metal strips. The polarization grating is set up between the horn antenna and the E-field probe. This experiment shows that the electric field vector of the radiated microwaves is perpendicular to the long side of the horn radiator. The second experiment deals with the absorption of microwaves. Working on the assumption that reflections may be ignored, the absorption in different materials is calculated using both the incident and the transmitted intensity. This experiment reveals a fact which has had a profound impact on modern cooking: microwaves are absorbed particularly intensively by water. In the third experiment, standing microwaves are generated by reflection at a metal plate. The intensity, measured at a fixed point between the horn antenna and the metal plate, changes when the metal plate is shifted longitudinally. The distance between two intensity maxima corresponds to one half the wavelength. Inserting a dielectric in the beam path shortens the wavelength. The next two experiments show that many of the properties of microwaves are comparable to those of visible light. The diffraction of microwaves at an edge, a single slit, a double slit and an obstacle are investigated. Additionally, the refraction of microwaves is demonstrated and the validity of Snell’s law of refraction is confirmed. The final experiment investigates total reflection of microwaves at media with lower refractive indices. We know from wave mechanics that the reflected wave penetrates about three to four wavelengths deep into the medium with the lower refractive index, before traveling along the boundary surface in the form of surface waves. This is verified in an experiment by placing an absorber (e.g. a hand) on the side of the medium with the lower refractive index close to the boundary surface and observing the decrease in the reflected intensity. P 3.7.4.2 P 3.7.4.3 P 3.7.4.4 P 3.7.4.5 P 3.7.4.6 P 3.7.4.1 137 Electromagnetic oscillations and waves P 3.7.5 Propagation of microwaves along lines P 3.7.5.1 Guiding of microwaves along a Lecher line P 3.7.5.2 Qualitative demonstration of guiding of microwaves through a flexible metal waveguide P 3.7.5.3 Determining the standing-wave ratio of a rectangular waveguide for a variable reflection factor Electricity Guiding of microwaves along a Lecher line (P 3.7.5.1) To minimize transmission losses over long distances, microwaves can also be transmitted along lines. For this application, metal waveguides are most commonly used; Lecher lines, consisting of two parallel wires, are less common. Despite this, the first experiment investigates the guiding of microwaves along a Lecher line. The voltage along the line is measured using the E-field probe. The wavelengths are determined from the spacing of the maxima. The second experiment demonstrates the guiding of microwaves along a hollow metal waveguide. First, the E-field probe is used to verify that the radiated intensity at a position beside the horn antenna is very low. Next, a flexible metal waveguide is set up and bent so that the microwaves are guided to the E-field probe, where they are measured at a greater intensity. Quantitative investigations on guiding microwaves in a rectangular waveguide are conducted in the third experiment. Here, standing microwaves are generated by reflection at a shorting plate in a waveguide, and the intensity of these standing waves is measured as a function of the location in a measuring line with movable measuring probe. The wavelength in the waveguide is calculated from the distance between two intensity maxima or minima. A variable attenuator is set up between the measuring line and the short which can be used to attenuate the intensity of the returning wave by a specific factor, and thus vary the standing-wave ratio. Cat. No. 737 01 737 020 737 021 737 03 737 06 737 09 737 095 737 10 737 111 737 14 737 15 737 21 737 275 737 35 737 399 737 27 531 100 309 06 578 300 11 301 21 501 01 501 02 501 022 501 461 737 390 Description Gunn oscillator Gunn power supply Gunn power supply with SWR meter Coax detector Isolator Variable attenuator Fixed attenuator Moveable short Slotted measuring line Waveguide termination Support for waveguide components Large horn antenna Physics microwave accessories II E-field probe Set of 10 thumb srcews M4 Physics microwave accessories I Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax2 Stand rod 245 mm, with thread Saddle base Stand base MF BNC cable, 0.25 m long BNC cable, 1 m long BNC cable, 2 m long Pair of cables, 1 m, black 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 2 2 1 2 1 I Set of absorbers *additionally recommended I 1* I I 1* I 1* 138 P 3.7.5.3 (b) 1 1 1 1 1 1 1 1 1 P 3.7.5.3 (a) P 3.7.5.2 P 3.7.5.1 Electricity Electromagnetic oscillations and waves P 3.7.6 Directional characteristic of dipole radiation P 3.7.6.1 Directional characteristic of a helical antenna – manual recording P 3.7.6.2 Directional characteristic of a Yagi antenna – manual recording P 3.7.6.3 Directional characteristic of a helical antenna – recording with a computer P 3.7.6.4 Directional characteristic of a Yagi antenna – recording with a computer Directional characteristic of a helical antenna – manual recording (P 3.7.6.1) Cat. No. 737 01 737 020 737 03 737 05 737 06 737 15 737 21 737 390 737 405 737 407 737 412 737 432 Description Gunn oscillator Gunn power supply Coax detector PIN modulator Isolator Support for waveguide components Large horn antenna Set of absorbers Rotating antenna platform Antenna stand with amplifier 1 1 1 1 1 1 1 1 1* 1* 1 1* 1* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Dipole antenna kit Yagi antenna kit Helical antenna kit Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax2 Stand base MF Saddle base BNC cable, 1 m long BNC cable, 2 m long Screened cable BNC/4 mm Pair of cables, 1 m, black additionally required: PC with Windows 95/NT or higher 1 1 2 1 1 737 440 531 100 301 21 300 11 501 02 501 022 575 24 501 461 1 1 2 1 1 1 1 2 1 1 2 309 06 578 I Stand rod 245 mm, with thread I 2I 2 I I *additionally recommended Directional antennas radiate the greater part of their electromagnetic energy in a particular direction and/or are most sensitive to reception from this direction. All directional antennas require dimensions which are equivalent to multiple wavelengths. In the microwave range, this requirement can be fulfilled with an extremely modest amount of cost and effort. Thus, microwaves are particularly suitable for experiments on the directional characteristics of antennas. In the first experiment, the directional characteristic of a helical antenna is recorded. As the microwave signal is excited with a linearly polarizing horn antenna, the rotational orientation of the helical antenna (clockwise or counterclockwise) is irrelevant. The measurement results are represented in the form of a polar diagram, from which the unmistakable directional characteristic of the helical antenna can be clearly seen. In the second experiment, a dipole antenna is expanded using parasitic elements to create a Yagi antenna, to improve the directional properties of the dipole arrangement. Here, a total of four shorter elements are placed in front of the dipole as directors, and a slightly longer element placed behind the dipole serves as a reflector. The directional factor of this arrangement is determined from the polar diagram. In the third and fourth experiment, the antennas are placed on a turntable which is driven by an electric motor; the angular turntable position is transmitted to a computer. The antennas receive the amplitude-modulated microwave signals, and frequency-selective and phase-selective detection are applied to suppress noise. The received signals are preamplified in the turntable. After filtering and amplification, they are passed on to the computer. For each measurement, the included software displays the receiving power logarithmically in a polar diagram. P 3.7.6.2 P 3.7.6.3 P 3.7.6.4 P 3.7.6.1 139 Free charge carriers in a vacuum P 3.8.1 Tube diode Electricity P 3.8.1.1 Recording the characteristic of a tube diode P 3.8.1.2 Half-wave rectification using a tube diode Recording the characteristic of a tube diode (P 3.8.1.1) A tube diode contains two electrodes: a heated cathode, which emits electrons due to thermionic emission, and an anode. A positive potential between the anode and the cathode generates an emission current to the anode, carried by the free electrons. If this potential is too low, the emission current is prevented by the space charge of the emitted electrons, which screen out the electrical field in front of the cathode. When the potential between the anode and the cathode is increased, the isoelectric lines penetrate deeper into the space in front of the cathode, and the emission current increases. This increase of the current with the potential is described by the Schottky-Langmuir law: IåU 3 2 Cat. No. 555 610 555 600 536 251 Description Demonstration diode tube Stand for electron tubes Measuring resistor 100 kOhm, 2 W 1 1 521 65 521 40 Tube power supply 0 .... 500 V Variable low voltage transformer 0 .... 250 V Ammeter, AC, I ≤ 10 mA, e.g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 500 V, e.g. Multimeter METRAmax 3 Two-channel oscilloscope 303 Probe, 100 MHz, 1:1 or 10:1 Screened cable BNC/4 mm 1 531 100 1 1 1 1 1 This current increases until the space charge in front of the cathode has been overcome and the saturation value of the emission current has been reached. On the other hand, if the negative potential applied to the anode is sufficient, the electrons cannot flow to the anode and the emission current is zero. In the first experiment, the characteristic of a tube diode is recorded, i.e. the emission current is measured as the function of the anode potential. By varying the heating voltage, it can be demonstrated that the saturation current depends on the temperature of the cathode. The second experiment demonstrates half-wave rectification of the AC voltage signal using a tube diode. For this experiment, an AC voltage is applied between the cathode and the anode via an isolating transformer, and the voltage drop is measured at a resistor connected in series. This experiment reveals that the diode blocks when the current is reversed. 531 712 575 211 575 231 575 24 500 641 500 642 Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue 3 4 140 P 3.8.1.2 1 1 1 P 3.8.1.1 1 1 2 3 Electricity Free charge carriers in a vacuum P 3.8.2 Tube triode P 3.8.2.1 Recording the characteristic field of a tube triode P 3.8.2.2 Amplifying voltages with a tube triode Recording the characteristic field of a tube triode (P 3.8.2.1) Cat. No. 555 612 555 600 Description Demonstration triode tube Stand for electron tubes Measuring resistor 100 kV, 2 W Function generator, S12, 0.1 Hz to 20 kHz 1 1 1 1 1 1 536 251 522 621 521 65 Tube power supply 0....500 V Ammeter, AC, I ≤ 1 mA, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 50 V, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 500 V, e. g. Multimeter METRAmax 3 Two-channel oscilloscope 303 Probe, 100 MHz, 1:1 or 10:1 Screened cable BNC/4 mm 1 1 531 100 531 100 531 712 575211 575 231 575 24 1 1 1 1 1 1 In a tube triode, the electrons pass through the mesh of a grid on their way from the cathode to the anode. When a negative voltage UG is applied to the grid, the emission current IA to the anode is reduced; a positive grid voltage increases the anode current. In other words, the anode current can be controlled by the grid voltage. The first experiment records the family of characteristics of the triode, i.e. the anode current IA as a function of the grid voltage UG and the anode voltage UA. The second experiment demonstrates how a tube triode can be used as an amplifier. A suitable negative voltage UG is used to set the working point of the triode on the characteristic curve IA(UA) so that the characteristic is as linear as possible in the vicinity of the working point. Once this has been set, small changes in the grid voltage FUG cause a change in the anode voltage FUA by means of a proportional change in the anode current FIA. The ratio: dUA V= dUG is known as the gain. P 3.8.2.1 500 622 500 641 500 642 Safety connection lead, 50 cm, blue Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue 1 5 5 2 3 3 P 3.8.2.2 Characteristic field of a tube triode 141 Free charge carriers in a vacuum P 3.8.3 Maltese-cross tube Electricity P 3.8.3.1 Demonstrating the linear propagation of electrons in a fieldfree space P 3.8.3.2 Deflection of electrons in an axial magnetic field Deflection of electrons in an axial magnetic field (P 3.8.3.2) In the Maltese cross tube, the electrons are accelerated by the anode to a fluorescent screen, where they can be observed as luminescent phenomena. A Maltese cross is arranged between the anode and the fluorescent screen, and its shadow can be seen on the screen. The Maltese cross has its own separate lead, so that it can be connected to any desired potential. The first experiment confirms the linear propagation of electrons in a field-free space. In this experiment, the Maltese cross is connected to the anode potential and the shadow of the Maltese cross in the electron beam is compared with the light shadow. We can conclude from the observed coincidence of the shadows that electrons propagate in a straight line. The Maltese cross is then disconnected from any potential. The resulting space charges around the Maltese cross give rise to a repulsive potential, so that the image on the fluorescent screen becomes larger. In the second experiment an axial magnetic field is applied using an electromagnet. The shadow cross turns and shrinks as a function of the coil current. When a suitable relationship between the high voltage and the coil current is set, the cross is focused almost to a point, and becomes larger again when the current is increased further. The explanation for this magnetic focusing may be found in the helical path of the electrons in the magnetic field. Cat. no. 555 620 555 600 555 604 Description Maltese cross tube Stand for electron tubes Pair of Helmholtz coils High voltage power supply 10 kV DC power supply 0...16 V, 5 A 1 1 521 70 521 545 1 510 48 500 611 500 621 500 622 500 641 500 642 500 644 Pair of magnets, cylindrical Safety connectin lead, 25 cm, red Safety connectin lead, 50 cm, red Safety connectin lead, 50 cm, blue Safety connectin lead, 100 cm, red Safety connectin lead, 100 cm, blue Safety connectin lead, 100 cm, black 1 1 1 1 2 1 1 1 2 2 2 2 Schematic diagram of Maltese cross tube 142 P 3.8.3.2 1 1 1 1 1 P 3.8.3.1 Electricity Free charge carriers in a vacuum P 3.8.4 Perrin tube P 3.8.4.1 Hot-cathode emission in a vacuum: determining the polarity and estimating the specific charge of the emitted charge carriers P 3.8.4.2 Generating Lissajou figures through electron deflection in crossed alternating magnetic fields Hot-cathode emission in a vacuum: determining the polarity and estimating the specific charge of emitted charge carriers (P 3.8.4.1) Cat. No. 500 622 500 600 500 604 562 14 521 35 Description Perrin tube Stand for electron tubes Pair of Helmholtz coils Coil with 500 turns Variable extra low-voltage transformer S 1 1 1 1 1 1 1 1 In the Perrin tube, the electrons are accelerated through an anode with iris diaphragm onto a fluorescent screen. Deflection plates are mounted at the opening of the iris diaphragm for horizontal electrostatic deflection of the electron beam. A Faraday’s cup, which is set up at an angle of 45° to the electron beam, can be charged by the electrons deflected vertically upward. The charge current can be measured using a separate connection. In the first experiment, the current through a pair of Helmholtz coils is set so that the electron beam is incident on the Faraday’s cup of the Perrin tube. The Faraday’s cup is connected to an electroscope which has been pre-charged with a known polarity. The polarity of the electron charge can be recognized by the direction of electroscope deflection when the Faraday’s cup is struck by the electron beam. At the same time, the specific electron charge can be estimated. The following relationship applies: e 2UA UA: anode voltage = m (B · r)2 The bending radius r of the orbit is predetermined by the geometry of the tube. The magnetic field B is calculated from the current I through the Helmholtz coils. In the second experiment, the deflection of electrons in crossed alternating magnetic fields and in coaxial alternating electric and magnetic fields is used to produce Lissajou figures on the fluorescent screen. This experiment demonstrates that the electrons respond to a change in the electromagnetic fields with virtually no lag. 521 70 521 545 522 621 High voltage power supply 10 kV DC power supply 0 ... 16 V, 5 A Function generator S 12, 0.1 Hz to 20 kHz 1 1 540 091 300 11 300 761 500 611 500 621 500 622 Electroscope Saddle base Support blocks, set of 6 pcs Safety connection lead, 25 cm, red Safety connection lead, 50 cm, red Safety connection lead, 50 cm, blue 1 1 1 1 2 1 4 2 2 1 2 1 3 3 2 500 641 500 642 500 644 Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue Safety connection lead, 100 cm, black P 3.8.4.2 1 1 P 3.8.4.1 143 Free charge carriers in a vacuum P 3.8.5 Thomson tube Electricity P 3.8.5.1 Investigating the deflection of electrons in electrical and magnetic fields P 3.8.5.2 Assembling a velocity filter (Wien filter) to determine the specific electron charge Investigating the deflection of electrons in electrical fields (P 3.8.5.1) In the Thomson tube, the electrons pass through a slit iris behind the anode and fall glancingly on a fluorescent screen placed in the beam path at an angle. A plate capacitor is mounted at the opening of the slit diaphragm which can electrostatically deflect the electron beam vertically. In addition, Helmholtz coils can be used to generate an external magnetic field which can also deflect the electron beam. The first experiment investigates the deflection of electrons in electric and magnetic fields. For different anode voltages UA, the beam path of the electrons is observed when the deflection voltage UP at the plate capacitor is varied. Additionally, the electrons are deflected in the magnetic field of the Helmholtz coils by varying the coil current I. The point at which the electron beam emerges from the fluorescent screen gives us the radius R of the orbit. When we insert the anode voltage in the following equation, we can obtain an experimental value for the specific electron charge e 2UA , = m (B · r)2 whereby the magnetic field B is calculated from the current I. In the second experiment, a velocity filter (Wien filter) is constructed using crossed electrical and magnetic fields. Among other things, this configuration permits a more precise determination of the specific electron charge. At a fixed anode voltage UA, the current I of the Helmholtz coils and the deflection voltage UP are set so that the effects of the electric field and the magnetic field just compensate each other. The path of the beam is then virtually linear, and we can say: 2 e 1 UP = · m 2UA B·d Cat. No. 555 624 555 600 555 604 Description Electron beam deflection tube Stand for electron tubes Pair of Helmholtz coils High voltage power supply 10 kV DC power supply 0...16 V, 5 A Safety connection lead, 25 cm, red Safety connection lead, 50 cm, red Safety connection lead, 50 cm, blue Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue Safety connection lead, 100 cm, black 521 70 521 545 500 611 500 621 500 622 500 641 500 642 500 644 3 2 ( ) d: plate spacing of the plate capacitor Deflection of electrons in magnetic fields 144 P 3.8.5.1-2 1 1 1 2 1 2 1 1 3 Electricity Electrical conduction in gases P 3.9.1 Self-maintained and nonself-maintained discharge P 3.9.1.1 Non-self-maintained discharge: comparing the charge transport in a gas triode and high-vacuum triode P 3.9.1.2 Ignition and extinction of selfmaintained gas discharge Non-self-maintained discharge: comparing the charge transport in a gas triode and high-vacuum triode (P 3.9.1.1) (a) (b) Cat. No. 500 614 500 612 555 600 Description Gas-filled triode Demonstration triode tube Stand for electron tubes Tube power supply 0....500 V Voltmeter, DC, U ≤ 500 V, e. g. Multimeter METRAmax 3 Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax 2 Ammeter, AC, I ≤ 50 mA, e. g. Multimeter METRAport 3E 1 1 1 1 1 1 1 1 1 1 521 65 531 712 531 100 531 57 1 1 1 1 1 1 2 1 500 641 500 642 Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue 6 4 5 3 5 3 A gas becomes electrically conductive, i. e. gas discharge occurs, when a sufficient number of ions or free electrons as charge carriers are present in the gas. As the charge carriers recombine with each other, new ones must be produced constantly. We speak of self-maintained gas discharge when the existing charge carriers produce a sufficient number of new charge carriers through the process of collision ionization. In non-self-maintained gas discharge, free charge carriers are produced by external effects, e. g. by the emission of electrons from a hot cathode. The first experiment looks at non-self-maintained gas discharge. The comparison of the current-voltage characteristics of a highvacuum triode and an He gas triode shows that additional charge carriers are created in a gas triode. Some of the charge carriers travel to the grid of the gas triode, where they are measured using a sensitive ammeter to determine their polarity. The second experiment investigates self-maintained discharge in an He gas triode. Without cathode heating, gas discharge occurs at an energizing voltage UZ which depends on the type of gas. This gas discharge also maintains itself at lower voltages, and only goes out when the voltage falls below the extinction voltage UL. Below the energizing voltage UZ, non-self-maintained discharge can be triggered, e. g. by switching on the cathode heating. P 3.9.1.2 P 3.9.1.1 145 Electrical conduction in gases P 3.9.2 Gas discharge at reduced pressure P 3.9.2.1 Investigating self-maintained discharge in air as a function of air pressure Electricity Investigating self-maintained discharge in air as a function of air pressure (P 3.9.2.1) Glow discharge is a special form of gas discharge. It maintains itself at low pressures with a relatively low current density, and is connected with spectacular luminous phenomena. Research into these phenomena provided fundamental insights into the structure of the atom. In this experiment, a cylindrical glass tube is connected to a vacuum pump and slowly evacuated. A high voltage is applied to the electrodes at the end of the glass tube. No discharge occurs at standard pressure. However, when the pressure is reduced to a certain level, current flows, and a luminosity is visible. When the gas pressure is further reduced, multiple phases can be observed: First, a luminous “thread” joins the anode and the cathode. Then, a column of light extends from the anode until it occupies almost the entire space. A glowing layer forms on the cathode. The column gradually becomes shorter and breaks down into multiple layers, while the glowing layer becomes larger. The layering of the luminous zone occurs because after collision excitation, the exciting electrons must traverse an acceleration distance in order to acquire enough energy to re-excite the atoms. The spacing of the layers thus illustrates the free path length. Cat. No. 554 161 378 752 378 764 378 015 378 023 378 045 378 050 378 776 378 777 378 500 378 501 378 502 378 701 521 70 Description Discharge tube, open Rotary-vane vacuum pump D 2.5 E Exhaust filter Cross DN 16 KF Male ground joint NS 19/26 Centering ring DN 16 KF Clamping ring DN 10/16 KF Variable leak valve DN 16 KF Ball valve with 2 flanges DN 16 KF Vacuum meter THERMOVAC TM 21 Gauge tube TR 211 Gauge head cable, 3 m High-vacuum grease P, 50 g High voltage power supply 10 kV 501 05 High voltage cable, 1 m * additionally recommended 146 P 3.9.2.1 1 1 1* 1 1 4 4 1 1 1 1 1 1 1 2 Electricity Electrical conduction in gases P 3.9.3 Cathode and canal rays P 3.9.3.1 Magnetic deflection of cathode and canal rays Magnetic deflection of cathode and canal rays (P 3.9.3.1) Cat. No. 554 161 378 752 378 764 378 015 378 023 378 045 378 050 378 776 378 777 378 500 378 501 378 502 Description Discharge tube, open Rotary-vane vacuum pump D 2.5 E Exhaust filter Cross DN 16 KF Male grount joint NS 19/26 Centering ring DN 16 KF Clamping ring DN 10/16 KF Variable leak valve DN 16 KF Ball valve with 2 flanges DN 16 KF Vacuum meter THERMOVAC TM 21 Gauge tube TR 211 Gauge head cable, 3 m 1 1 1* 1 1 4 4 1 1 1 1 1 Cathode and canal rays can be observed in a gas discharge tube which contains only a residual pressure of less than 0.1 mbar. When a high voltage is applied, more and more electrons are liberated from the residual gas on collision with the cathode. The electrons travel to the anode virtually unhindered, and some of them manage to pass through a hole to the glass wall behind it. Here they are observed as fluorescence phenomena. The luminousity also appears behind the cathode, which is also provided with a hole. A tightly restricted canal ray consisting of positive ions passes straight through the hole until it hits the glass wall. In this experiment, the cathode rays, i. e. the electrons, and the canal rays are deflected using a magnet. From the observation that the deflection of the canal rays is significantly less, we can conclude that the ions have a lower specific charge. 378 701 521 70 510 48 501 05 High-vacuum grease P, 50 g High voltage power supply 10 kV Pair of magnets, cylindrical High voltage cable, 1 m 1 1 1 2 * additionally recommended P 3.9.3.1 147 Electronics Table of contents Electronics P4 Electronics P 4.1 P 4.1.1 P 4.1.2 P 4.1.3 P 4.1.4 P 4.1.5 P 4.1.6 P 4.1.7 Components and basic circuits Current and voltage sources Special resistors Diodes Diode circuits Transistors Transistor circuits Optoelectronics 151–152 153 154 155 156 157 158 P 4.4 P 4.4.1 P 4.4.2 P 4.4.3 P 4.4.4 P 4.4.5 P 4.4.6 Digital technology Basic logical operations Switching networks and units Serial and parallel arithmetic units Digital control systems Structure of a central processing unit (CPU) Microprocessor 163 164 165 166 167 168 P 4.2 P 4.2.1 P 4.2.2 Operational amplifier Internal design of an operational amplifier Operational amplifier circuits 159 160 P 4.3 P 4.3.1 P 4.3.2 Open- and closed-loop control Open-loop control Closed-loop control 161 162 150 Electronics Components and basic circuits P 4.1.1 Current and voltage sources P 4.1.1.1 P 4.1.1.2 Determining the internal resistance of a battery Operating a DC power supply as a constant-current and constant-voltage source Determining the internal resistance of a battery (P 4.1.1.1) Cat. No. 576 89 503 11 521 50 531 100 531 100 531 712 537 32 501 23 501 25 501 26 501 30 501 31 Description Battery case 2 x 4.5 Volt Set of 20 batteries 1.5 V (type MONO) AC/DC power supply 0....15 V Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 3 A, e. g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 6 A, e. g. Multimeter METRAmax 3 Rheostat 10 V Connecting lead, Ø 2.5 mm2, 25 cm, black Connecting lead, Ø 2,5 mm2, 50 cm, red Connecting lead, Ø 2,5 mm2, 50 cm, blue Connecting lead, Ø 2.5 mm2, 100 cm, red Connecting lead, Ø 2.5 mm2, 100 cm, blue * additionally recommended 1 1 1 1 1 1* 1 5 1* 1* 1 1 1 The voltage U0 generated in a voltage source generally differs from the terminal voltage U measured at the connections as soon as a current I is drawn from the voltage source. A resistance Ri must therefore exist within the voltage source, across which a part of the generated voltage drops. This resistance is called the internal resistance of the voltage source. In the first experiment, a rheostat as an ohmic load is connected to a battery to determine the internal resistance. The terminal voltage U of the battery is measured for different loads, and the voltage values are plotted over the current I through the rheostat. The internal resistance Ri is determined using the formula U = U0 – Ri · I by drawing a best-fit straight line through the measured values. A second diagram illustrates the power P=U·I as a function of the load resistance. The power is greatest when the load resistance has the value of the internal resistance Ri. The second experiment demonstrates the difference between a constant-voltage source and a constant-current source using a DC power supply in which both modes are implemented. The voltage and current of the power supply are limited to the respective values U0 and I0. The terminal voltage U and the current I consumed are measured for various load resistances R. When the load resistance R is reduced, the terminal voltage retains a constant value U0 as long as the current I remains below the set limit value I0. The DC power supply operates as a constant-voltage source with an internal resistance of zero. When the load resistance R is increased, the current consumed remains constant at I0 as long as the terminal voltage does not exceed the limit value U0. The DC power supply operates as a constant-current source with infinite internal resistance. P 4.1.1.2 P 4.1.1.1 151 Components and basic circuits P 4.1.1 Current and voltage sources P 4.1.1.3 Recording the current-voltage characteristics of a solar battery as a function of the irradiance Electronics Recording the curent-voltage characteristics of a solar battery as a function of the irradiance (P 4.1.1.3) The solar cell is a semiconductor photoelement in which irradiance is converted directly to electrical energy at the p-n junction. Often, multiple solar cells are combined to create a solar battery. In this experiment the current-voltage characteristics of a solar battery are recorded for different irradiance levels. The irradiance is varied by changing the distance of the light source. The characteristic curves reveal the characteristic behavior. At a low load resistance, the solar battery supplies an approximately constant current. When it exceeds a critical voltage (which depends on the irradiance), the solar battery functions increasingly as a constant-voltage source. Cat. No. 578 63 576 74 576 77 577 90 501 48 531 100 531 100 450 64 450 63 521 25 300 11 501 45 501 461 Description STE solar battery 2 V / 0.3 A Plug-in board, DIN A4 Pair of holders for rastered socket panel STE potentiometer 220 V, 3 W Set of 10 bridging plugs Voltmeter, DC, U ≤ 3 V, e. g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 200 mA, e. g. Multimeter METRAmax 2 Halogen lamp housing 12 V, 50/100W Halogen lamp, 12 V/100 W Transformer 2 ....12 V Saddle base Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, black Current-voltage characteristics for different illuminance levels 152 P 4.1.1.3 1 1 1 1 1 1 1 1 1 1 1 2 1 Electronics Components and basic circuits P 4.1.2 Special resistors P 4.1.2.1 Recording the current-voltage characteristic of an incandescent lamp P 4.1.2.2 Recording the current-voltage characteristic of a varistor P 4.1.2.3 Measuring the temperaturedependency of PTC and NTC resistors P 4.1.2.4 Measuring the light-dependency of photoresistors Recording the current-voltage characteristic of an incandescent lamp (P 4.1.2.1) Cat. No. 505 08 505 13 576 71 577 98 578 00 578 02 578 04 578 06 579 05 521 545 521 210 Description Set of 10 lamps E 10; 12 V/3 W Lamp with socket E 10; 6.0 V/5.0 W Plug-in board section STE Resistor 1 E, 0.5 W STE VDR-resistor STE photoresistor LDR 05 STE NTC probe 4.7 kE STE PTC probe 30 E STE lamp holder, E10, lateral DC power supply 0....16 V, 5A Transformer, 6 V AC,12 V AC/30 VA Voltmeter, DC, U ≤ 20 V, e. g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 3 A, e.g. Multimeter METRAmax 2 Power-CASSY CASSY Lab Steel tape measure, 2 m Thermometer, -10° to + 110 °C Hot plate, 150 mm dia., 1500 W Beaker, 400 ml, ss, hard glass Connecting lead, red 100 cm Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, black additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 531 100 531 100 524 011 524 200 311 77 382 34 666 767 664 104 500 441 501 45 501 461 1 1 1 1 1 2 1 2 1 1 Many materials do not conduct voltage and current in proportion to one another. Their resistance depends on the current level. In technical applications, elements in which the resistance depends significantly on the temperature, the luminous intensity or another physical quantity are increasingly important. In the first experiment, the computer-assisted measured-value recording system CASSY is used to record the current-voltage characteristic of an incandescent lamp. As the incandescent filament heats up when current is applied, and its resistance depends on the temperature, different characteristic curves are generated when the current is switched on and off. The characteristic also depends on the rate of increase dU/dt of the voltage. The second experiment records the current-voltage characteristic of a varistor (voltage dependent resistor). Its characteristic is non-linear in its operating range. At higher currents, it enters the so-called “rise range", in which the ohmic component of the total resistance increases. The aim of the third experiment is to measure the temperature characteristics of an NTC thermistor resistor and a PTC thermistor resistor. The respective measured values can be described using empirical equations in which only the rated value R0, the reference temperature T0 and a material constant appear as parameters. The subject of the final experiment is the characteristic of a CdS light-dependent resistor. Its resistance varies from approx. 100 V to approx. 10 MV, depending on the brightness. The resistance is measured as a function of the distance from an incandescent lamp which illuminates the light-dependent resistor. P 4.1.2.2 P 4.1.2.3 579 06 I Lamp holder E10, top, STE I 1I I I P 4.1.2.4 P 4.1.2.1 153 Components and basic circuits P 4.1.3 Diodes Electronics P 4.1.3.1 Recording the current-voltage characteristics of diodes P 4.1.3.2 Recording the current-voltage characteristics of zener diodes P 4.1.3.3 Recording the current-voltage characteristics of light-emitting diodes (LEDs) Recording the current-voltage characteristics of light-emitting diodes (LEDs) (P 4.1.3.3) Virtually all aspects of electronic circuit technology rely on semiconductor components. The semiconductor diodes are among the simplest of these. They consist of a semiconductor crystal in which an n-conducting zone is adjacent to a p-conducting zone. Capture of the charge carriers, i.e. the electrons in the n-conducting and the “holes” in the p-conducting zones, forms a lowconductivity zone at the junction called the depletion layer. The size of this zone is increased when electrons or holes are removed from the depletion layer by an external electric field with a certain orientation. The direction of this electric field is called the reverse direction. Reversing the electric field drives the respective charge carriers into the depletion layer, allowing current to flow more easily through the diode. In the first experiment, the current-voltage characteristics of an Si-diode (silicon diode) and a Ge-diode (germanium diode) diode are measured and graphed manually point by point. The aim is to compare the current in the reverse direction and the threshold voltage as the most important specifications of the two diodes. The objective of the second experiment is to measure the current-voltage characteristic of a zener or Z-diode. Here, special attention is paid to the breakdown voltage in the reverse direction, as when this voltage level is reached the current rises abruptly. The current is due to charge carriers in the depletion layer, which, when accelerated by the applied voltage, ionize additional atoms of the semiconductor through collision. The final experiment compares the characteristics of infrared, red, yellow and green light-emitting diodes. The threshold voltage U is inserted in the formula c e·U=h· Ö e: electron charge, c: velocity of light, h: Planck’s constant, to estimate the wavelength Ö of the emitted light. P 4.1.3.2 1 1 1 1 1 1 1 1 2 Cat. No. 576 74 577 32 578 57 578 47 578 48 578 49 578 50 578 51 578 54 578 55 521 48 531 100 Description Rastered socket panel, DIN A4 STE Resistor 100 E, 2 W STE light emitting diode LD 57 C, green STE light emitting diode yellow, LED 3, top STE light emitting diode red, LED 2, top STE light emitting diode LD 271 H, infrared STE Ge-diode AA 118 STE Si-diode 1 N 4007 STE Z-diode ZPD 9.1 STE Z-diode ZPD 6.2 AC/DC-Power supply, 0....12 V, 230 V/50 Hz Voltmeter, DC, U ≤ 10 V, e.g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 150 mA, e.g. Multimeter METRAmax 2 Connecting lead, red 100 cm Pair of cables, 50 cm, red and blue 1 1 1 1 1 1 1 1 2 531 100 500 441 501 45 154 P 4.1.3.3 1 1 1 1 1 1 1 1 1 1 2 P 4.1.3.1 Electronics Components and basic circuits P 4.1.4 Diode circuits P 4.1.4.1 Rectification of AC voltages with diodes P 4.1.4.2 Limiting voltages with a Z-diode P 4.1.4.3 Testing polarity with light emitting diodes. Rectification of AC voltages with diodes (P 4.1.4.1) Cat. No. 576 74 577 42 578 48 578 57 578 51 578 55 579 06 501 48 505 08 521 48 575 211 575 24 531 100 531 100 501 45 Description Plug-in board, DIN A4 STE resistor 680 E, 2 W STE light emitting diode red, LED 2, top STE light emitting diode LD 57 C, green STE Si-diode 1 N 4007 STE Z-diode ZPD 6.2 STE lamp holder, E10, top Set of 10 bridging plubs Set of 10 lamps E 10; 12 V/3.0 W AC/DC power supply 0....12 V, 230 V/50 Hz Two channel oscilloscope 303 Screened cable BNC/4 mm Voltmeter, AC/DC, U ≤ 12 V, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 12 V, e. g. Multimeter METRAmax 2 Pair of cables, 50 cm, red and blue 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 2 2 3 1 1 1 1 1 Diodes, zener diodes (or Z-diodes) and light-emitting diodes are used today in virtually every electronic circuit. The first experiment explores the function of half-wave and fullwave rectifiers in the rectification of AC voltages. The half-wave rectifier assembled using a single diode blocks the first half-wave of every AC cycle and conducts only the second half-wave (assuming the diode is connected with the corresponding polarity). The full-wave rectifier, assembled using four diodes in a bridge configuration, uses both half-waves of the AC voltage. The second experiment demonstrates how a Z-diode can be used to protect against voltage surges. As long as the applied voltage is below the breakdown voltage UZ of the Z-diode, the Zdiode acts as an insulator and the voltage U is unchanged. At voltages above UZ, the current flowing through the Z-diode is so high that U is limited to UZ. The aim of the last experiment is to assemble a circuit for testing the polarity of a voltage using a green and a red light emitting diode (LED). The circuit is tested with both DC and AC voltage. P 4.1.4.2 P 4.1.4.3 P 4.1.4.1 155 Components and basic circuits P 4.1.5 Transistors Electronics P 4.1.5.1 Investigating the diode characteristics of transistor junctions P 4.1.5.2 Recording the characteristics of a transistor P 4.1.5.3 Recording the characteristics of a field-effect transistor Recording the characteristics of a transistor (P 4.1.5.2) Transistors are among the most important semiconductor components in electronic circuit technology. We distinguish between bipolar transistors, in which the electrons and holes are both involved in conducting current, and field-effect transistors, in which the current is carried solely by electrons. The electrodes of a bipolar transistor are called the emitter, the base and the collector. The transistor consists of a total of three n-conducting and p-conducting layers, in the order npn or pnp. The base layer, located in the middle, is so thin that charge carriers originating at one junction can cross to the other junction. In field-effect transistors, the conductivity of the current-carrying channel is changed using an electrical field, without applying power. The element which generates this field is called the gate. The input electrode of a field-effect transistor is known as the source, and the output electrode is called the drain. The first experiment examines the principle of the bipolar transistor and compares it with a diode. Here, the difference between an npn and a pnp transistor is explicitly investigated. The second experiment examines the properties of an npn transistor on the basis of its characteristics. This experiment measures the input characteristic, i. e. the base current IB as a function of the base-emitter voltage UBE, the output characteristic, i. e. the collector current IC as a function of the collector-emitter voltage UCE at a constant base current IB and the collector current IC as a function of the base current IB at a constant collectoremitter voltage UCE . In the final experiment, the characteristic of a field-effect transistor, i. e. the drain current ID, is recorded and diagrammed as a function of the voltage UDS between the drain and source at a constant gate voltage UG. P 4.1.5.2 1 1 1 1 1 1 1 1 2 1 1 4 Cat. No. 576 74 577 32 577 44 577 64 577 90 577 92 578 67 578 68 578 77 578 51 501 48 521 48 521 45 521 210 Description Plug-in board, DIN A4 STE resistor 100 Ω, 2 W STE resistor 1 kΩ, 2 W STE resistor 47 kΩ, 0,5 W STE potentiometer 220 Ω, 3 W STE potentiometer 1 kΩ, 1 W STE transistor BD 137, NPN, emitter bottom STE transistor BD 138, PNP, emitter bottom STE transistor BF 244 (FET) STE Si-diode 1 N 4007 Set of 10 bridging plugs AC/DC power supply 0....12 V, 230 V/50 Hz DC power supply 0 ... ± 15 V Transformer, 6 V ~, 12 V ~/ 30 W Ammeter, DC, I ≤ 100 mA, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 12 V, e. g. Multimeter METRAmax 2 Two-channel oscilloscope 303 Screened cable BNC/4 mm Connecting lead, blue, 50 cm Pair of cables, 50 cm, red and blue 1 1 1 1 1 531 100 531 100 575 211 575 24 500 422 501 45 1 1 3 156 P 4.1.5.3 1 1 1 1 1 1 1 1 1 P 4.1.5.1 1 1 1 1 1 2 1 3 Electronics Components and basic circuits P 4.1.6 Transistor circuits P 4.1.6.1 Transistor as amplifier P 4.1.6.2 Transistor as switch P 4.1.6.3 Transistor as sine-wave generator (oscillator) P 4.1.6.4 Transistor as function generator P 4.1.6.5 Field-effect transistor as amplifier P 4.1.6.6 Field-effect transistor as switch Transistor as amplifier (P 4.1.6.1) Cat. No. Description 576 74 578 67 578 76 Rastered socket panel DIN A4 1 1 1 1 1 1 1 1 1 STE transistor BD 137, NPN, emitter bottom 1 STE transistor BC 140, NPN, emitter bottom 2 1 1 Transistor circuits are investigated on the basis of a number of examples. These include the basic connections of a transistor as an amplifier, the transistor as a light-dependent or temperaturedependent electronic switch, the Wien bridge oscillator as an example of a sine-wave generator, the astable multivibrator, basic circuits with field-effect transistors as amplifiers as well as the field-effect transistor as a low-frequency switch. P 4.1.6.1(b) P 4.1.6.1(a) P 4.1.6.1(b) P 4.1.6.1(a) P 4.1.6.2 P 4.1.6.3 P 4.1.6.4 P 4.1.6.5 1 578 762 STE transistor BC 140, NPN, emitter top 578 77 577 44 577 46 577 56 577 58 577 61 577 64 577 657 577 68 577 76 577 80 577 81 577 82 577 92 578 02 578 06 578 13 578 16 578 22 578 23 578 33 578 35 578 36 578 38 STE FET transistor BF 244 STE resistor 1 kE, 2 W STE resistor 1.5 kE, 2 W STE resistor 10 kE, 0.5 W STE resistor 15 kE, 0.5 W STE resistor 33 kE, 0.5 W STE resistor 47 kE, 0.5 W STE resistor 68 kE, 0.5 W STE resistor 100 kE, 0.5 W STE resistor 1 ME, 0.5 W STE regulation resistor 10 kE, 1 W STE regulation resistor 4.7 kE, 1 W STE regulation resistor 47 kE, 1 W STE regulation resistor 1 kE, 1 W STE photoresistor LDR 05 STE PTC probe 30 W STE capacitor 0.22 µF, 250 V STE capacitor 4.7 µF, 63 V STE capacitor 100 pF, 630 V STE capacitor 220 pF, 160 V STE capacitor 0.47µF, 100 V STE capacitor 1 µF, 100 V STE capacitor 2.2 µF, 63 V STE electrolytic capacitor 47 µF, 40 V 1 1 2 2 2 3 1 1 1 1 1 1 1 2 2 1 1 2 1 1 3 2 1 1 1 2 P 4.1.6.6 P 4.1.6.2 P 4.1.6.3 P 4.1.6.4 P 4.1.6.5 1 1 1 1 2 1 1 2 Cat. No. Description 2 1 2 1 1 1 1 1 1 1 578 39 578 40 578 41 578 51 579 06 579 13 579 38 501 48 505 08 505 19 1 522 621 STE electrolytic capacitor 100 µF, 35 V STE electrolytic capacitor 470 µF, 16 V STE electrolytic capacitor 220 µF, 35 V STE Si-diode 1 N 4007 STE Lamp holder E10, top STE toggle switch, single-pole STE heating element, 100 W, 2 W Set of 10 bridging plugs Set of 10 lamps E 10; 12 V/3 W Glow lamp E 10; 15 V/2.0 W 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 Function generator S 12, 0.1 Hz to 20 kHz 1 AC/DC power supply 0....12 V, 230 V/50 Hz DC power supply 0....+/- 15 V 1 521 48 521 45 1 575 211 575 24 1 2 1 1 501 45 501 451 1 1 1 1 Two-channel oscilloscope 303 Screened cable BNC/4 mm Connecting lead, Ø 2.5 mm2, 50 cm, black Pair of cables, 50 cm, red and blue Pair of cables, 50 cm, black 1 2 1 2 2 1 2 1 1 1 2 1 3 1 531 100 Multimeter METRAmax 2 501 28 1 1 1 1 4 2 157 P 4.1.6.6 1 1 1 2 1 1 2 1 Components and basic circuits P 4.1.7 Optoelectronics Electronics P 4.1.7.1 P 4.1.7.2 Recording the characteristics of a phototransistor connected as a photodiode Assembling a purely optical transmission line Assembling a purely optical transmission line (P 4.1.7.2) Optoelectronics deals with the application of the interactions between light and electrical charge carriers in optical and electronic devices. Optoelectronic arrangements consist of a lightemitting, a light-transmitting and a light-sensitive element. The light beam is controlled electrically. The subject of the first experiment is a phototransistor without base terminal connection used as a photodiode. The currentvoltage characteristics are displayed on an oscilloscope for the unilluminated, weakly illuminated and fully illuminated states. It is revealed that the characteristic of the fully illuminated photodiode is comparable with that of a Z-diode, while no conducting-state behavior can be observed in the unilluminated state. The second experiment demonstrates optical transmission of the electrical signals of a function generator to a loudspeaker. The signals modulate the light intensity of an LED by varying the onstate current; the light is transmitted to the base of a phototransistor via a flexible light waveguide. The phototransistor is connected in series to the speaker, so that the signals are transmitted to the loudspeaker. P 4.1.7.1 (b) 1 1 1 1 1 1 1 2 1 1 2 P 4.1.7.1 (a) Cat. No. Description 578 68 STE transistor BD 138, PNP, emitter bottom 578 85 577 28 577 32 577 40 577 44 577 48 577 56 577 64 578 16 578 39 578 40 579 05 505 08 521 48 521 45 521 210 STE operational amplifier LM 741 STE resistor 47 E, 2 W STE resistor 100 E, 2 W STE resistor 470 E, 2 W STE resistor 1 kE 2 W STE resistor 2.2 kE, 2 W STE resistor 10 kE, 0.5 W STE resistor 47 kE, 0.5 W STE capacitor 4.7 µF, 63 V STE electrolytic capacitor 100 µF, 35 V STE electrolytic capacitor 470 µF, 16 V STE lamp holder E 10, lateral Set of 10 lamps E 10, 12 V/3 W AC/DC power supply 0....12 V, 230 V/50 Hz DC power supply 0....+/- 15 V Transformer, 6 V AC,12 V AC/30 VA Two-channel oscilloscope 303 Screened cable BNC/4 mm Ammeter, DC, I ≤ 150 mA, e.g. Multimeter METRAmax 2 Earphone, 2 kE Function generator S 12, 0.1 Hz to 20 kHz Set of 10 bridging plugs Pair of cables, 50 cm, red and blue Connection lead, 50 cm, black Connection lead, 25 cm, black 1 2 1 2 1 1 1 1 1 1 575 211 575 24 P 4.1.7.1 (b) P 4.1.7.1 (a) P 4.1.7.2 531 100 579 29 522 621 Cat. No. Description 576 74 578 57 578 58 578 61 Rastered socket panel, DIN A4 STE light emitting diode LD 57C, green STE light emitting diode CQV 51J, red STE photodiode BPX 43 1 1 1 1 1 501 48 501 45 500 424 500 414 1 1 1 158 P 4.1.7.2 1 1 1 1 1 1 3 1 2 1 1 1 1 1 1 2 1 3 Electronics Operational amplifier P 4.2.1 Internal design of an operational amplifier P 4.2.1.1 Discrete assembly of an operational amplifier as a transistor circuit Discrete assembly of an operational amplifier as a transistor circuit (P 4.2.1.1) Cat. No. 576 75 577 04 577 07 577 10 577 20 577 36 577 38 577 40 577 44 577 52 577 93 578 31 578 39 578 51 578 55 578 69 578 71 578 72 501 48 521 45 Description Rastered socket panel, DIN A3 STE resistor 1 kE, 0.5 W STE resistor 10 kE, 0.5 W STE resistor 100 kE, 0.5 W STE resistor 10 E, 2 W STE resistor 220 E, 2 W STE resistor 330 E, 2 W STE resistor 470 E, 2 W STE resistor 1 kE, 2 W STE resistor 4.7 kE, 2 W STE 10-turn potentiometer 1 kE, 2 W STE capacitor 0.1 µF, 100 V STE electrolytic capacitor 100 µF, 35 V STE Si-diode 1 N 4007 STE Z-diode ZPD 6.2 STE transistor BC 550, NPN, emitter bottom STE transistor BC 550, NPN, emitter top STE transistor BC 560, PNP, emitter top Set of 10 bridging plugs DC power supply 0....+/- 15 V 2 4 3 1 3 1 1 1 4 2 1 2 1 4 1 3 1 1 5 1 Many electronics applications place great demands on the amplifier. The ideal characteristics include an infinite input resistance, an infinitely high voltage gain and an output voltage which is independent of load and temperature. These requirements can be satisfactorily met using an operational amplifier. In this experiment, an operational amplifier is assembled from discrete elements as a transistor circuit. The key components of the circuit are a difference amplifier on the input side and an emitter-follower stage on the output side. The gain and the phase relation of the output signals are determined with respect to the input signals in inverting and non-inverting operation. This experiment additionally investigates the frequency characteristic of the circuit. P 4.2.1.1 1 1 2 5 2 1 1+1* Circuit diagram of an operational amplifier assembled from discrete components 522 621 Function generator S 12, 0.1 Hz to 20 kHz Two-channel oscilloscope 303 Screened cable BNC/4 mm Connecting lead, black, 25 cm Connecting lead, black, 50 cm Connecting lead, black, 100 cm Pair of cables, 50 cm, red and blue Pair of cables, 1 m, red and blue Multimeter with diode tester, e.g. Analog-digital multimeter C.A 5011 575 211 575 24 500 414 500 424 500 444 501 45 501 46 531 181 1 1* * additionally recommended 159 Operational amplifier P 4.2.2 Operational amplifier circuits P 4.2.2.1 Unconnected operational amplifier (comparator) P 4.2.2.2 Inverting operational amplifier P 4.2.2.3 Non-inverting operational amplifier P 4.2.2.4 Adder and subtracter P 4.2.2.5 Differentiator and integrator Electronics Adder and subtracter (P 4.2.2.4) The first experiment shows that the unconnected operational amplifier overdrives for even the slightest voltage differential at the inputs. It generates a maximum output signal with a sign corresponding to that of the input-voltage differential. In the second and third experiments, the output of the operational amplifier is fed back to the inverting and non-inverting inputs via resistor R2. The initial input signal applied via resistor R1 is amplified in the inverting operational amplifier by the factor R V= – 2 R1 and in the non-inverting module by the factor R V= 2 + 1 R1 The fourth experiment demonstrates the addition of multiple input signals and the subtraction of input signals. The aim of the final experiment is to use the operational amplifier as a differentiator and an integrator. For this purpose, a capacitor is connected to the input resp. the feedback loop of the operational amplifier. The output signals of the differentiator are proportional to the change in the input signals, and those of the integrator are proportional to the integral of the input signals. P 4.2.2.2 P 4.2.2.3 P 4.2.2.4 1 1 1 1 1 1 2 1 1 4 1 1 Cat. No. 576 74 578 85 577 32 577 38 577 40 577 44 577 46 577 48 577 50 577 52 577 56 577 58 577 60 577 61 577 62 577 64 577 68 577 74 577 76 577 80 577 96 578 15 Description Plug-in board, DIN A4 STE operational amplifier LM 741 STE resistor 100 E, 2 W STE resistor 330 E, 2 W STE resistor 470 E, 2 W STE resistor 1 kE, 2 W STE resistor 1.5 kE, 2 W STE resistor 2.2 kE, 2 W STE resistor 3.3 kE, 2 W STE resistor 4.7 kE, 2 W STE resistor 10 kE, 0.5 W STE resistor 15 kE, 0.5 W STE resistor 22 kE, 0.5 W STE resistor 33 kE, 0.5 W STE resistor 39 kE, 0.5 W STE resistor 47 kE, 0.5 W STE resistor 100 kE, 0.5 W STE resistor 470 kE, 0.5 W STE resistor 1 ME, 0.5 W STE regulation resistor 10 kE, 1 W STE potentiometer 100 kE, 1 W STE capacitor 1 µF, 100 V STE capacitor 4.7 µF, 63 V STE capacitor 2.2 nF, 160 V STE capacitor 10 nF, 100 V STE Si diode 1 N 4007 STE transistor BC 140, NPN, emitter bottom Set of 10 bridging plugs DC power supply 0....+/- 15 V 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P 4.2.2.2 P 4.2.2.3 P 4.2.2.4 P 4.2.2.5 P 4.2.2.1 578 16 578 26 578 28 578 51 578 76 501 48 521 45 Cat. No. 522 621 Description Function generator S 12, 0.1 Hz to 20 kHz Two-channel oscilloscope 303 Screened cable BNC/4 mm Multimeter METRAport 3E Connection lead, 50 cm, black 1 1 2 1 1 2 1 1 1 2 1 9 1 1 2 1 8 7 575 211 575 24 531 57 500 424 8 8 160 P 4.2.2.5 1 1 1 1 1 P 4.2.2.1 Electronics Open- and closed-loop control P 4.3.1 Open-loop control P 4.3.1.1 Assembling a traffic-light control system P 4.3.1.2 Assembling a model for control of stairway illumination Assembling a traffic-light control system (P 4.3.1.1) Cat. No. 576 74 579 06 579 10 579 18 579 36 501 48 505 08 505 07 521 48 501 46 501 461 Description Rastered socket panel, DIN A4 STE lamp socket E 10, top STE key switch n.o. single-pole STE dual program disk with cams STE motor 12 V /4 W, with gear Set of 10 bridging plugs Set of 10 lamps E 10; 12 V/3 W Set of 10 lamps E 10; 4.0 V/0.16 W AC/DC power supply 0....12 V, 230 V/50 Hz Pair of cables, 100 cm, red and blue Pair of cables, 100 cm, black 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 “Control” is the term for any process in which the input variables of a system influence the output variables. The type of influence depends on the individual system. In the first experiment, the red, yellow and green phases of a traffic light are controlled cyclically by means of three cam disks driven by a common shaft. Here, the elastic switching tabs are actuated as the on and off switches for the individual lights. When the cam disks are provided with the appropriate pluggable cams, the three phases of the traffic light are controlled in a sensible sequence. The second experiment examines how a stairway illumination system is controlled. Pressing a pushbutton switches on the lighting and the drive motor of the cam disk at the same time. Both remain on for a period which is determined by the number of cams attached to the disk. P 4.3.1.2 P 4.3.1.1 161 Open- and closed-loop control P 4.3.2 Closed-loop control Electronics P 4.3.2.1 Assembling a model for servo control P 4.3.2.2 Brightness control with CASSY P 4.3.2.3 Voltage control with CASSY Voltage control with CASSY (P 4.3.2.3) P 4.3.2.1(b) P 4.3.2.1(a) P 4.3.2.1(b) P 4.3.2.1(a) P 4.3.2.2 P 4.3.2.3 P 4.3.2.2 1 1 1 1 1 1 2 1* 1* 1 Cat. No. Description Cat. No. Description 576 74 576 75 577 07 577 15 577 19 577 20 577 48 577 68 577 76 577 78 577 79 577 81 578 02 578 28 521 45 Rastered socket panel, DIN A4 Rastered socket panel, DIN A3 STE resistor 10 kΩ, 0.5 W STE resistor 0.1 Ω, 2 W STE resistor 1 Ω, 2 W STE resistor 10 Ω, 2 W STE resistor 2.2 kΩ, 2 W STE resistor 100 kΩ, 0.5 W STE resistor 1 MΩ, 0.5 W STE resistor 10 MΩ, 0.5 W STE regulation resistor 1 kΩ, 1 W STE regulation resistor 4.7 kΩ, 1 W STE photoresistor LDR 05 STE capacitor 10 nF, 100 V 1 3 3 1 1 1 1 1 1 2 1 1 578 31 578 35 STE capacitor 0.1 µF, 100 V STE capacitor 1 µF, 100 V STE power OP amp TCA 365 STE lamp socket E 10, side STE lamp socket E 10, top STE toggle switch, single pole STE motor and tachogenerator STE potentiometer 4.7 kΩ, 2 W STE motor potentiometer 4.7 kΩ, 2 W Set of 10 bridging plugs Set of 10 lamps E 10; 3.8 V/0.27 W Lamp with socket, E 10; 6.0 V/5.0 W Power CASSY Current supply box Sensor CASSY CASSY Lab Two-channel oscilloscope 303 Screened cable BNC/4 mm Plastic tubing, 6 mm int. dia. Pair of cables, 100 cm, red and blue Set 30 connecting leads Pair of cables, 50 cm, red and blue Function generator S 12, 0.1 Hz to 20 kHz additionally required: 1 PC with Windows 95/NT or higher * additionally recommended 2 1 1 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 578 86 579 05 579 06 579 13 579 43 581 43 581 49 501 48 505 10 505 13 524 011 524 031 1 1 2 1 1 2 1 1 I DC power supply 0...+/-15 V I 1 I 1 I I 524 010 524 200 In the first experiment, a model of a servo control is assembled which consists of a P-controller with downstream operating amplifier as power controller, a set-point potentiometer and a motor potentiometer as servo drive. The aim of the two other experiments is the computer-aided realization of closed control loops. In the one case, a PI controller is assembled and used to control an incandescent lamp whose brightness is measured using a photoresistor. The other configuration controls a generator which supplies a constant voltage independently of the load. 575 211 575 24 307 641 501 46 501 532 501 45 522 56 1 2 1 2 1 2 1 1 162 P 4.3.2.3 3 1 2 1 1 1 1 Electronics Digital technology P 4.4.1 Basic logical operations P 4.4.1.1 AND, OR, XOR, NOT, NAND and NOR operations with two variables P 4.4.1.2 De Morgan's laws P 4.4.1.3 Operations with three variables AND, OR, XOR, NOT, NAND and NOR operations with two variables (P 4.4.1.1) Cat. No. Description 571 011 571 29 522 33 571 21 571 22 571 23 SIMULOG LS-TTL, P 1 Basic logic circuits Base plate DIN A 4 for SIMULOG LS-TTL Regulated power supply, 2 x 5 V DC/1.0 A Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm 1 1 1 1 1 1 Digital devices are built on the simple concept of repeated application of just a few basic circuits. Operations using these circuits are governed by the rules of Boolean algebra, sometimes also called “logic algebra” when applied to digital circuit technology. The first experiment introduces all operations with one or two variables used in digital technology. The aim is to verify the laws which apply in Boolean algebra, i. e. those describing commutation, idempotents, absorption and negation. The second experiment demonstrates de Morgan's laws in practical application. The object of the final experiment is to verify the associative and distributive laws through experiment when operating three variables. P 4.4.1.1-3 163 Digital technology P 4.4.2 Combinatorial and sequential circuits P 4.4.2.1 AND, NAND, OR and NOR operations with four variables P 4.4.2.2 Coders, decoders and code converters P 4.4.2.3 Multiplexers and demultiplexers P 4.4.2.4 Adders P 4.4.2.5 Flipflops P 4.4.2.6 Counters P 4.4.2.7 Shift registers Electronics 4-bit digital counter (P 4.4.2.6) A combinatorial circuit performs operations on multiple digital circuits such that the output variables are uniquely determined by the input variables. A sequential circuit is additionally able to store the states of individual variables. The output variables also depend on the result of preceding events, which is represented by the switching state of flipflops. As an approach to the structure of complex combinatorial circuits, the first experiment applies the understanding of basic operations previously learned to the logical operation of four inputs. Combinatorial circuits for coding and decoding signals are the theme of the second experiment. In this experiment, the object is to assemble a coder for coding decimal numbers in binary form, a corresponding decoder and a code converter for converting binary to Gray code. The third experiment demonstrates how a multiplexer is used to switch multiple inputs onto a single output and a demultiplexer distributes the signals of a single input line to multiple output lines. The fourth experiment investigates half adders, full adders and parallel adders as key components of a computer. The aim of the fifth experiment is to study the function of flipflops. It deals with the various demands on the behavior of these fundamental components of sequential circuits, which are required for assembling RS, D and JK flipflops. The sixth experiment gives the students an opportunity to assemble various synchronous and asynchronous counters. Specifically, these include a binary counter, a BCD counter, a 4-bit counter, a forward-reverse counter and a counter with parallel data input. The final experiment investigates the shift register as a further important function group in data-processing systems. This experiment shows how these components can be used to realize multiplication and division of binary numbers in an extremely easy fashion. 164 Cat. No. Description 571 011 571 022 571 29 571 21 571 22 571 23 571 24 522 33 SIMULOG LS-TTL, P 1 basic logic circuits SIMULOG LS-TTL, extension P 2 switching networks and units Base plate DIN A 4 for SIMULOG LS-TTL Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm Set of 5 connecting leads, 30 cm Regulated power supply, 2 x 5 V DC/1.0 A P 4.4.2.1-7 1 1 1 2 2 2 1 1 Electronics Digital technology P 4.4.3 Serial and parallel arithmetic units P 4.4.3.1 Data transfer between registers P 4.4.3.2 Serial and parallel logic elements P 4.4.3.3 Serial and parallel adders and subtracters P 4.4.3.4 Functions of the buffer, latch and accumulator Serial and parallel adders and subtracters (P 4.4.3.3) Cat. No. 571 011 571 022 571 044 571 29 522 33 571 21 571 22 571 23 571 24 Description SIMULOG LS-TTL, P 1 basic logic circuits SIMULOG LS-TTL extension P 2 switching networks and units SIMULOG LS-TTL extension E 4 serial and parallel arithmetic units Base plate DIN A4 for SIMULOG LS-TTL Regulated power supply, 2 x 5 V DC/1.0 A Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm Set of 5 connecting leads, 30 cm 1 1 1 1 1 4 2 2 2 In information technology, the hardware executes arithmetic, Boolean and other operations using arithmetic units. The operations can be performed either serially or in parallel. The first three experiments investigate the serial and parallel processing of data in registers, logic elements and adders and subtracters. The final experiment demonstrates the function of the buffer as a bus driver, the latch as a small intermediate storage element and the accumulator as a register which supports arithmetic operations. P 4.4.3.1-4 165 Digital technology P 4.4.4 Digital control systems Electronics P 4.4.4.1 Structure of functional circuits P 4.4.4.2 DA and AD converter Setup for measuring reaction times (P 4.4.4.1) Digital control units are used increasingly in industrial applications in order to realize periodic processes reliably and without the need for a great deal of complex circuitry. In the first experiment, the object is to assemble functional digital circuits for controlling a traffic light, an LED display with hexadecimal display, a digital clock with decimal display of seconds and an alarm system. The second experiment investigates the function of an analogdigital and a digital-analog converter which allow digital and analog units to be integrated in an industrial open control loop. Cat. No. 571 011 571 022 571 033 571 29 571 98 571 99 571 21 571 22 571 23 571 24 571 25 522 33 Description SIMULOG LS-TTL, P 1 basic logic circuits SIMULOG LS-TTL, extension P 2 switching networks and units SIMULOG LS-TTL, extension E 3, digital measurements and control circuits Base plate DIN A 4 for SIMULOG LS-TTL IC-socket, 14 pin, top IC-socket, 16 pin, top Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm Set of 5 connecting leads, 30 cm Set of 5 connecting leads, 50 cm Regulated power supply, 2 x 5 V DC/1.0 A 166 P 4.4.4.1-2 1 1 1 1 1 1 5 3 2 2 1 1 Electronics Digital technology P 4.4.5 Structure of a central processing unit (CPU) P 4.4.5.1 Function of the ALU, CPU timer, RAM und I/O components P 4.4.5.2 Address bus and data bus P 4.4.5.3 Indirect, direct and immediate addressing P 4.4.5.4 Conditional and unconditional jump instructions P 4.4.5.5 Program memory P 4.4.5.6 Examples of programs Structure of a central processing unit (CPU) (P 4.4.5.1) Cat. No. Description 571 099 571 28 522 33 571 21 571 22 571 23 571 24 571 25 SIMULOG LS-TTL, kit C 9 (complete kit) assembly of a central unit Base plate DIN A3 for SIMULOG LS-TTL Regulated power supply, 2 x 5 V DC/1.0 A Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm Set of 5 connecting leads, 30 cm Set of 5 connecting leads, 50 cm 1 1 1 9 4 12 5 2 The heart of every information processing system is the central processing unit (CPU). This consists of an arithmetic and logic unit (ALU), a control unit, the registers and the working memory (RAM), as well as the input and output modules. These elements are linked via the bus system. The structure of the CPU is determined mainly by the requirements of the software. The first experiment explores the functions of the individual hardware components of a CPU, while the second experiment investigates the organization of the address and data buses. The aim of the third experiment is to illustrate the difference between indirect, direct and immediate addressing of storage locations in arithmetic and logic operations. The fourth experiment shows how a predefined program sequence can be altered using conditional and unconditional jump instructions. The fifth experiment looks at how to assemble and expand the program memory. Finally, simple program examples are realized in the last experiment. P 4.4.5.1-6 167 Digital technology P 4.4.6 Microprocessor Electronics P 4.4.6.1 Signal transmission via the address, data and control buses P 4.4.6.2 Program counter and address structure, zero page P 4.4.6.3 Data-transfer instructions P 4.4.6.4 Rotation and shift instructions P 4.4.6.5 Arithmetic and logic operations P 4.4.6.6 Program control using jumps, branches, subprogram calls and interrupt processing P 4.4.6.7 Application examples Assembly with microprocessor (P 4.4.6.7) The microprocessor BP 6502 is used as the basis for the stepby-step investigation of the main structures and functions of a real microprocessor with input/output units, address-bus display and working memory. Here, the special properties of microprocessors are of course taken into account. The first experiment comprises introductory demonstrations on signal transmission via the address, data and control buses. The second experiment illustrates the function of the program counter, which counts one address further each time an instruction is read. In addition, the division of the 16-bit wide addresses into pages and the storage capacity of each page are examined, as well as the special importance of the zero page. The third experiment focuses on the various data-transfer instructions of the processor and demonstrates how each one is used. This is followed in the fourth experiment by the investigation of processing instructions which shift the content of a register one bit to the right or the left, so that a ninth bit, the carry flag, is required to accommodate the carry digit. The aim of the fifth experiment is to perform arithmetic and logic operations on two register contents. The final two experiments illustrate the control of complex programs. Jump instructions enable the creation of a program loop as well as the subsequent return. Branching instructions make it possible to make the program dependent on a condition. Subprogram calls, as the name implies, permit special subprograms to be activated repeatedly from various points in the main program. Interrupt processing enables a defined interruption of the program flow in such a way that the program can be resumed at the same point. Cat. No. Description 571 088 571 28 522 33 571 21 571 22 571 23 571 24 571 25 SIMULOG LS-TTL, kit M 8 (complete kit) microprocessor circuits Base plate DIN A3 for SIMULOG LS-TTL Regulated power supply, 2 x 5 V DC/1.0 A Set of 5 connecting leads, 4 cm Set of 5 connecting leads, 8 cm Set of 5 connecting leads, 15 cm Set of 5 connecting leads, 30 cm Set of 5 connecting leads, 50 cm 168 P 4.4.6.1-7 1 1 1 6 3 4 2 3 Optics Table of contents Optics P5 Optics P 5.1 P 5.1.1 P 5.1.2 P 5.1.3 P 5.1.4 Geometrical optics Reflection and diffraction Laws of imaging Image distortion Optical instruments 171 172 173 174 P 5.5 P 5.5.1 P 5.5.2 Light intensity Quantities and measuring methods of lighting engineering Laws of radiation 194 195 P 5.6 P 5.2 P 5.2.1 P 5.2.2 P 5.2.3 P 5.2.4 Velocity of light Measurement according to Foucault and Michelson Measuring with short light pulses Measuring with an electronically modulated signal 196 197 198 Dispersion and chromatics Refractive index and dispersion Decomposition of white light Color mixing Absorption spectra 175 176 177 178 P 5.6.1 P 5.6.2 P 5.6.3 P 5.3 P 5.3.1 P 5.3.2 P 5.3.3 P 5.3.4 P 5.3.5 P 5.3.6 P 5.3.7 Wave optics Diffraction Two-beam interference Newton's rings Michelson interferometer Mach-Zehnder interferometer White-light reflection holography Transmission holography 179–180 182 183 184 185 186 187 P 5.7 P 5.7.1 P 5.7.2 Spectrometer Prism spectrometer Grating spectrometer 199 200–201 P 5.4 P 5.4.1 P 5.4.2 P 5.4.3 P 5.4.4 P 5.4.5 P 5.4.6 Polarization Basic experiments Birefringence Optical activity, polarimetry Kerr effect Pockels effect Faraday effect 188 189 190 191 192 193 170 Optics Geometrical optics P 5.1.1 Reflection, refraction P 5.1.1.1 P 5.1.1.2 Reflection of light at straight and curved mirrors Refraction of light at straight surfaces and investigation of ray paths in prisms and lenses Refraction (reflection) of light (P 5.1.1.1, P 5.1.1.2) Cat. No. Description 463 52 450 60 450 51 521 210 Optical disk with 8 model objects Lamp housing Lamp, 6 V/30 W Transformer, 6 V AC, 12 V AC/30 VA Small optical bench Diaphragm with 5 slits Lens f = + 150 mm Stand base, V-shape, 28 cm Leybold multiclamp Stand rod, 25 cm 1 1 1 1 1 1 1 1 4 1 460 43 463 51 460 08 300 01 301 01 300 41 Frequently, the propagation of light can be adequately described simply by defining the ray path. Examples of this are the ray paths of light in mirrors, in lenses and in prisms using sectional models. The first experiment examines how a mirror image is formed by reflection at a plane mirror and demonstrates the reversibility of the ray path. The law of reflection is experimentally validated: a=b a: angle of incidence, b: angle of reflection Further experiment objectives deal with the reflection of a parallel light beam in the focal point of a concave mirror, the existence of a virtual focal point for reflection in a convex mirror, the relationship between focal length and bending radius of the curved mirror and the creation of real and virtual images for reflection at a curved mirror. The second experiment deals with the change of direction when light passes from one medium into another. The law of refraction discovered by W. Snell is quantitatively verified: sin a n2 = sin b n1 a: angle of incidence, b: = angle of refraction, n1: refractive index of medium 1 (here air), n2: refractive index of medium 2 (here glass) This experiment topic also studies total reflection at the transition from a medium with a greater refractive index to one with a lesser refractive index, the concentration of a parallel light beam at the focal point of a collecting lens, the existence of a virtual focal point when a parallel light beam passes through a dispersing lens, the creation of real and virtual images when imaging with lenses and the ray path through a prism. P 5.1.1.1–2 171 Geometrical optics P 5.1.2 Laws of imaging Optics P 5.1.2.1 Determining the focal lengths at collecting and dispersing lenses using collimated light P 5.1.2.2 Determining the focal lengths at collecting lenses through autocollimation P 5.1.2.3 Determining the focal lengths at collecting lenses using Bessel’s method P 5.1.2.4 Verifying the imaging laws with a collecting lens Determining the focal lengths at collecting lenses using Bessel’s method (P 5.1.2.3) The focal lengths of lenses are determined by a variety of means. The basis for these are the laws of imaging. In the first experiment, an observation screen is set up parallel to the optical axis so that the path of a parallel light beam can be observed on the screen after passing through a collecting or dispersing lens. The focal length is determined directly as the distance between the lens and the focal point. In autocollimation, a parallel light beam is reflected by a mirror behind a lens so that the image of an object is viewed right next to that object. The distance d between the object and the lens is varied until the object and its image are exactly the same size. At this point, the focal length is: f=d In the Bessel method, the object and the observation screen are set up at a fixed overall distance s apart. Between these points there are two lens positions x1 and x2 at which a sharply focused image of the object is produced on the observation screen. From the lens laws, we can derive the following relationship for the focal length: f= 1 · 4 Cat. No. Description 450 51 450 60 460 20 521 210 Lamp, 6 V/30 W Lamp housing Aspherical condenser Transformer, 6 V AC, 12 V AC/30 W Lens f = + 50 mm Lens f = + 100 mm Lens f = + 150 mm Lens f = + 200 mm Lens f = + 300 mm Lens f = - 100 mm Set of two transparencies Plane mirror with ball joint Translucent screen Small optical bench Stand base, V-shape, 20 cm Leybold multiclamp Steel tape measure, 2 m 1 1 1 1 1 1 1 1 1 1 460 02 460 03 460 08 460 04 460 09 460 06 461 66 460 28 441 53 460 43 300 02 301 01 311 77 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 3 1 1 ( s– (x1 – x2)2 s ) In the final experiment, the object height G, the object width g, the image height B and the image width b are measured directly for a collecting lens in order to confirm the lens laws. The focal length can be calculated using the formula: f= g·b g+b 172 P 5.1.2.3–4 1 1 1 1 1 1 P 5.1.2.2 P 5.1.2.1 Optics Geometrical optics P 5.1.3 Image distortion P 5.1.3.1 Spherical aberration and coma in lens imaging P 5.1.3.2 Astigmatism and curvature of image field in lens imaging P 5.1.3.3 Lens imaging distortions (barrel and cushion) P 5.1.3.4 Chromatic aberration in lens imaging Spherical aberration and coma in lens imaging (P 5.1.3.1) Cat. No. 461 61 461 66 467 95 450 60 450 51 460 20 521 210 Description Pair of stops for spherical aberration Set of 2 transparencies Filter set red, green, blue Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC / 30 W Lens, f = + 150 mm Iris diaphragm Translucent screen Small optical bench Stand base, V-shape, 20 cm Leybold multiclamp * additionally recommended 1 1 1 1 1 1* 1 1 1 1 1 1 4 1 1 1* 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 4 460 08 460 26 441 53 460 43 300 02 301 01 A spherical lens only images a point in an ideal point when the imaging ray traces intersect the optical axis at small angles, and the angle of incidence and angle of refraction are also small when the ray passes through the lens. As this condition is only fulfilled to a limited extent in practice, aberrations (image defects) are unavoidable. The first two experiments deal with aberrations of image sharpness. In a ray path parallel to the optical axis, paraxial rays are united at a different distance from abaxial rays. This effect, known as “spherical aberration”, is particularly apparent in lenses with sharp curvatures. “Coma” is the term for one-sided, plume-like or blob-like distortion of the image when imaged by a beam of light passing through the lens at an oblique angle. Astigmatism and curvature of field may be observed when imaging long objects with narrow light beams. The focal plane is in reality a curved surface, so that the image on the observation screen becomes increasingly fuzzy toward the edges when the middle is sharply focused. Astigmatism is the phenomenon whereby a tightly restricted light beam does not produce a point-type image, but rather two lines which are perpendicular to each other with a finite spacing with respect to the axis. The third experiment explores aberrations of scale. An iris diaphragm directly in front of or behind the imaging lenses causes distortions of the image. Blocking light rays in front of the lens causes a barrel-shaped distortion, i. e. a reduction in the imaging scale with increasing object size. Screening behind the lens results in cushion-type aberrations. The fourth experiment examines chromatic aberrations. These are caused by a change in the refractive index with the wavelength, and are thus unavoidable when not working with nonmonochromatic light. P 5.1.3.2 P 5.1.3.3 Intersections of paraxial and abaxial rays P 5.1.3.4 P 5.1.3.1 173 Geometrical optics P 5.1.4 Optical instruments Optics P 5.1.4.1 Magnifier and microscope P 5.1.4.2 Kepler’s telescope and Galileo’s telescope Kepler’s telescope (P 5.1.4.2) The magnifier, the microscope and the telescope are introduced as optical instruments which primarily increase the angle of vision. The design principle of each of these instruments is reproduced on the optical bench. For quantitative conclusions, the common definition of magnification is used: tanc c: angle of vision with instrument V= tanG G: angle of vision without instrument In the first experiment, small objects are observed from a short distance. First, a collecting lens is used as a magnifier. Then, a microscope in its simplest form is assembled using two collecting lenses. The first lens, the objective, produces a real, magnified and inverted intermediate image. The second lens, the ocular (or eyepiece) is used as a magnifier to view this intermediate image. For the total magnification of the microscope, the following applies: VM = Vob · Voc Vob: imaging scale of objective, Voc: imaging scale of ocular. Here, Voc corresponds to the magnification of the magnifier. s s0: clear field of vision, Voc = 0 foc foc: focal length of ocular. The aim of the second experiment is to observe distant objects using a telescope. The objective and the ocular of a telescope are arranged so that the back focal point of the objective coincides with the front focal point of the ocular. A distinction is made between the Galilean telescope, which uses a dispersing lens as an ocular and produces an erect image, and the Kepler telescope, which produces an inverted image because its ocular is a collecting lens. In both cases, the total magnification can be determined as: f fob: focal length of objective, VT = ob foc: focal length of ocular. foc Cat. No. 450 60 450 51 460 20 521 210 Description Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC / 30 W Holder with spring clips Glass scale, 5 cm long Lens, f = + 50 mm Lens, f = + 100 mm Lens, f = + 150 mm Lens, f = + 200 mm Lens, f = + 500 mm Lens, f = – 100 mm Precision optical bench, standardized cross section, 1 m Optics rider, H = 60 mm/W = 36 mm Optics rider, H = 60 mm/W = 50 mm Translucent screen Vertical scale, 1 m long Saddle base 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1 1 1 2 1 1 1 460 22 311 09 460 02 460 03 460 08 460 04 460 05 460 06 460 32 460 353 460 351 441 53 311 22 300 11 Ray path through the Kepler telescope 174 P 5.1.4.2 P 5.1.4.1 Optics Dispersion, chromatics P 5.2.1 Refractive index and dispersion P 5.2.1.1 Determining the refractive index and dispersion of flint glass and crown glass P 5.2.1.2 Determining the refractive index and dispersion of liquids Determining the refractive index and dispersion of liquids (P 5.2.1.2) Cat. No. 465 22 465 32 465 51 460 25 460 22 450 60 450 51 460 20 521 210 Description Crown glass prism Flint glass prism Hollow prism Prism table Holder with spring clips Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformator, 6 V AC,12 V AC /30 VA Monochromatic light filter, red Monochromatic light filter, yellow/green Monochromatic light filter, blue with violet Lens, f = + 150 mm Small optical bench Leybold multiclamp Stand base, V-shape, 28 cm Steel tape measure, 2m Toluol, 250 ml Terpentine oil, rectified, 250 ml Cinnamil ether, 100 ml Funnel, 50 mm dia., glass 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 Dispersion is the term for the fact that the refractive index n is different for different-colored light. Often, dispersion also refers to the quantity dn/dl, i. e. the quotient of the change in the refractive index dn and the change in the wavelength dl. P 5.2.1.2 P 5.2.1.1 468 03 468 07 468 11 460 08 460 43 301 01 300 01 311 77 675 2100 675 0410 675 4760 665 003 In the first experiment, the angle of minimum deviation G is determined for a flint glass and a crown glass prism at the same refracting angle Z. This enables determination of the refractive index of the respective prism material according to the formula sin 1 (e + f) 2 sin 1 e 2 n= The measurement is conducted for several different wavelengths, so that the dispersion can also be quantitatively measured. In the second experiment, an analogous setup is used to investigate dispersion in liquids. Toluol, turpentine oil, cinnamic ether, alcohol and water are each filled into a hollow prism in turn, and the differences in the refractive index and dispersion are observed. 175 Dispersion, chromatics P 5.2.2 Dispersion of white light Optics P 5.2.2.1 Newton’s experiments on dispersion and recombination of white light P 5.2.2.2 Adding complementary colors to create white light Newton’s experiment on the non-dispersable nature of spectral colors (P 5.2.2.1) The discovery that white sunlight is made up of light of different colors was one of the great milestones toward understanding the perception of color. Isaac Newton, in particular, conducted numerous experiments on this topic. Cat. No. 465 32 465 25 460 25 450 51 450 60 460 20 521 210 Description Flint glass prism Narrow prism on base Prism table Lamp, 6 V/30 W Lamp housing Aspherical condensor Transformer, 6 V AC, 12 V AC / 30 W Lens, f = + 100 mm Iris diaphragm Holder with spring clips Translucent screen Small optical bench Leybold multiclamp Rotatable clamp Stand rod, right-angled Stand base, V-shape, 28 cm 2 2 1 1 1 1 460 03 460 26 460 22 441 53 460 43 301 01 1 1 1 5 2 1 1 1 1 1 7 The first experiment topic looks at Newton’s experiments on the decomposition of a beam of white light using the light of an incandescent light bulb. In the first step, the white light is broken down into its spectral components in a glass prism. The second step shows that the dispersed light cannot be broken down further by a second prism. If only one spectral component is allowed to pass through a slit behind the first prism, the second prism will deviate this light, but will not break it down further. Using an assembly of two crossed prisms with the refracting edges perpendicular to each other provides additional confirmation of this principle. The vertical spectrum behind the first prism is deviated obliquely by the second prism, as the spectral colors are not broken down further by the second prism. The fourth step demonstrates the recombination of spectral colors to create white light by viewing the spectrum behind the first prism through a second prism arranged parallel to the first. 301 03 300 51 300 01 The second experiment also uses the color spectrum of an incandescent light bulb. This experiment starts with the recombination of the spectrum in a collecting lens to create white light. Subsequent screening of individual spectral ranges using an extremely narrow prism produces two images of different colors, which partially overlap on the observation screen. The colors can be varied by laterally shifting the narrow prism. The overlap field is white, which means that the respective complementary colors are projected next to each other on the screen. 176 P 5.2.2.2 1 1 2 1 1 1 1 1 1 P 5.2.2.1 Optics Dispersion, chromatics P 5.2.3 Color mixing P 5.2.3.1 Additive and subtractive color mixing Additive and subtractive color mixing (P 5.2.3.1) Cat. No. 466 16 466 15 452 111 Description Apparatus for additive color mixing Apparatus for subtractive color mixing Overhead projector Famulus alpha 250 1 1 1 300 43 300 01 Stand rod, 75 cm Stand base, V-shape, 28 cm 1 1 The apparatus for additive color mixing contains three color filters with the primary colors red, green and yellow. The colored light is made to overlap either partially or completely using mirrors. In the areas of overlap, additive color mixing creates the colors cyan (green + blue), magenta (blue + red) and yellow (red + green), and in the middle white (red + blue + green). The apparatus for subtractive color mixing contains three color filters with the colors cyan, magenta and yellow. The filters partially overlap; in the overlap zones, the three primary colors blue, red and green, and in the middle, black, are formed. Additive color mixing P 5.2.3.1 Subtractive color mixing 177 Dispersion, chromatics P 5.2.4 Absorption spectra Optics P 5.2.4.1 Absorption spectra of tinted glass samples P 5.2.4.2 Absorption spectra of colored liquids Absorption spectra of tinted glass samples (P 5.2.4.1) The colors we perceive when looking through colored glass or liquids are created by the transmitted component of the spectral colors. In both experiments, the light passing through colored pieces of glass or colored liquids from an incandescent light bulb is viewed through a direct-vision prism and compared with the continuous spectrum of the lamp light. The original, continuous spectrum with the continuum of spectral colors disappears. All that remains is a band with the color components of the filter or liquid. Cat. No. Description 466 050 477140 467 960 468 010 468 090 468 110 460 220 460 250 450 600 450 510 460 200 521 210 Direct vision prism Plate glass cell 50 x 50 x 20 mm Filter set yellow, cyan, magenta Monochromatic light filter, dark red Monochromatic light filter, blue/green Monochromatic light filter, blue with violet Holder with spring clips Prism table Lamp housing Lamp, 6 V/30 W Aspherical condenser Transformer, 6 V AC, 12 V AC/30 VA 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 2 1 1 1 1 1 1 1 5 1 1 441 530 460 030 460 430 301 010 300 010 672 7010 Translucent screen Lens f = + 100 mm Small optical bench Leybold multilamp Stand base, V-shape, 28 cm Potassium permanganate, 250 g Absorption spectra of tinted glass samples (without filter set yellow, cyan, magenta) 178 P 5.2.4.2 1 1 P 5.2.4.1 Optics P 5.3.1 Diffraction Wave optics P 5.3.1.1 Diffraction at a slit, at a post and at a circular iris diaphragm P 5.3.1.2 Diffraction at a double slit and at multiple slits P 5.3.1.3 Diffraction at one- and twodimensional gratings Diffraction at a double slit (P 5.3.1.2) Cat. No 469 91 469 96 469 97 469 84 469 85 469 86 469 87 469 88 471 830 460 22 460 01 460 02 460 32 460 353 441 53 300 11 Description Diaphragm with 3 single slits Diaphragm with 3 circular holes Diaphragm with 3 fine lines Diaphragm with 3 double slits Diaphragm with 4 double slits Diaphragm with 5 multiple slits Diaphragm with 3 gratings Diaphragm with 2 wire-mesh gratings He-Ne laser 0.2 /1 mW max., linearly polarized Holder with spring clips Lens, f = + 5 mm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 Lens, f = + 50 mm Precision optical bench, standardized cross section, 1 m 1 Optics rider, H = 60 mm/W = 36 mm Translucent screen Saddle base 4 1 1 The first experiment looks at the intensity minima for diffraction at a slit. Their angles Gk with respect to the optical axis for a slit of the width b is given by the relationship Ö sin Gk = k · (k = 1; 2; 3; . . . ) b Ö: wavelength of the light In accordance with Babinet’s theorem, diffraction at a post produces similar results. In the case of diffraction at a circular iris diaphragm with the radius r, concentric diffraction rings may be observed; their intensity minima can be found at the angles Gk using the relationship Ö sin Gk = k · (k = 0.610; 1.116; 1.619; . . . ) r The second experiment explores diffraction at a double slit. The constructive interference of secondary waves from the first slit with secondary waves from the second slit produces intensity maxima; at a given distance d between slit midpoints, the angles Gn of these maxima are specified by Ö sin Gn = n · (n = 0; 1; 2; . . . ) d The intensities of the various maxima are not constant, as the effect of diffraction at a single slit is superimposed on the diffraction at a double slit. In the case of diffraction at more than two slits with equal spacings d, the positions of the interference maxima remain the same. Between any two maxima, we can also detect N-2 secondary maxima; their intensities decrease for a fixed slit width b and increasing number of slits N. The third experiment investigates diffraction at a line grating and a crossed grating. We can consider the crossed grating as consisting of two line gratings arranged at right angles to each other. The diffraction maxima are points at the “nodes” of a straight, square matrix pattern. P 5.3.1.2 P 5.3.1.3 P 5.3.1.1 179 Wave optics P 5.3.1 Diffraction Optics P 5.3.1.4 Diffraction at a single slit – measuring and evaluating with CASSY P 5.3.1.5 Diffraction at multiple slits – measuring and evaluating with CASSY Diffraction at a single slit – measuring and evaluating with CASSY (P 5.3.1.4) A photoelement with a narrow light opening is used to measure the diffraction intensities; this sensor can be moved perpendicularly to the optical axis on the optical bench, and its lateral position can be measured using a displacement transducer. The measured values are recorded and evaluated using the software Universal Data Acquisition. The first experiment investigates diffraction at slit of variable width. The recorded measured values for the intensity I are compared with the results of a model calculation for small diffraction angles G which uses the slit width b as a parameter: sin öb f l Ia öb f l P 5.3.1.4 1 1 1 1 1 1 1 1 4 Cat. No. 460 14 471 830 460 01 460 02 469 84 469 85 469 86 460 22 Description Adjustable slit He-Ne laser 0.2/1 mW max., linearly polarized Lens, f = + 5 mm Lens, f = + 50 mm Diaphragm with 3 double slits Diaphragm with 4 double slits Diaphragm with 5 multiple slits Holder with spring clips STE photoelement Holder for plug-in elements Precision optical bench, standardized cross section, 1 m Auxiliary bench w. swivel joint, protractor and index bench, 0.5 m Rider 90/50 ( ) ( ) ( ) 2 where f = s L 578 62 460 21 460 32 460 34 460 352 460 355 524 010 524 040 524 031 529 031 524 200 301 07 309 48 342 61 l: wavelength of the light, s: lateral shift of photoelement, L: distance between diffraction object and photoelement. The second experiment explores diffraction at multiple slits. In the model calculation performed for comparison purposes, the slit width b and the slit spacing d are both used as parameters. sin öb f l la öb f l Sliding rider Sensor-CASSY mV-box Current supply box Displacement sensor CASSY Lab Simple bench clamp Cord, 10 m Set of 12 weights, 50 g each Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 2 1 ( )( 2 l ·a sin Nöd f l sin öd f l ( ( ) ) ) 2 N: number of illuminated slits. 501 46 180 P 5.3.1.5 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 2 1 Optics P 5.3.1 Diffraction Wave optics P 5.3.1.6 Diffraction at a single slit – measuring and evaluating with VideoCom P 5.3.1.7 Diffraction at multiple slits – measuring and evaluating with VideoCom P 5.3.1.8 Diffraction at a half-plane – measuring and evaluating with VideoCom Diffraction at a single slit (P 5.3.1.6, top) and at a half-plane (P 5.3.1.8, bottom) Cat. No. 460 14 469 84 469 85 469 86 471 830 472 401 460 01 460 02 460 11 460 22 460 32 460 351 337 47 Description Adjustable slit Diaphragm with 3 double slits Diaphragm with 4 double slits Diaphragm with 5 multiple slits He-Ne laser 0.2/1 mW max., linearly polarized Polarization filter Lens, f = + 5 mm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 7 1 1 1 1 6 1 1 1 1 Lens, f = + 50 mm Lens, f = + 500 mm Holder with spring clips Precision optical bench, standardized cross section, 1 m Optics rider, H = 60 mm/W = 50 mm VideoCom additionally required: PC with Windows 95 or Windows NT 1 1 1 Diffraction at a single slit or multiple slits can also be measured as a one-dimensional spatial intensity distribution using the singleline CCD camera VideoCom (here used without the camera lens). The VideoCom software enables fast, direct comparison of the measured intensity distributions with model calculations in which the wavelength Ö, the focal length f of the imaging lens, the slit width b and the slit spacing d are all used as parameters. These parameters agree closely with the values arrived at through experiment. It is also possible to investigate diffraction at a half-plane. Thanks to the high-resolution CCD camera, it becomes easy to follow the intensity distribution over more than 20 maxima and minima and compare it with the result of a model calculation. The model calculation is based on Kirchhoff’s formulation of Huygens’ principle. The intensity I at point x in the plane of observation is calculated from the amplitude of the electric field strength E at this point using the formula l (x) = | E(x) |2 The field strength is obtained through the phase-correct addition of all secondary waves originating from various points x’ in the diffraction plane, from the half-plane boundary x’ = 0 to x’ = ∞ E(x) Ù ∫ exp ( i · G (x, x’) ) · dx’ 0 ∞ P 5.3.1.6 P 5.3.1.7 P 5.3.1.8 Here, G(x, x’) = 2S Ö · (x – x’)2 2L is the phase shift of the secondary wave which travels from point x’ in the diffraction plane to point x in the observation plane as a function of the direct wave. The parameters in the model calculation are the wavelength Ö and the distance L between the diffraction plane and the observation plane. Here too, the agreement with the values obtained in the experiment is close. Measured (black) and calculated (red) intensity distributions (P 5.3.1.6, P 5.3.1.8) 181 Wave optics P 5.3.2 Two-beam interference Optics P 5.3.2.1 Interference at a Fresnel’s mirror with an He-Ne laser P 5.3.2.2 Lloyd’s mirror experiment with an He-Ne laser P 5.3.2.3 Interference at Fresnel’s biprism with an He-Ne laser Interference at a Fresnel’s mirror with an He-Ne laser (P 5.3.2.1) In these experiments, two coherent light sources are generated by recreating three experiments of great historical significance. In 1821, A. Fresnel used two mirrors inclined with respect to one another to create two virtual light sources positioned close together, which, being coherent, interfered with each other. In 1839, H. Lloyd demonstrated that a second, virtual light source coherent with the first can be created by reflection in a mirror. He observed interference phenomena between direct and reflected light. Coherent light sources can also be produced using a Fresnel biprism, first demonstrated in 1826. Refraction in both halves of the prism results in two virtual images, which are closer together the smaller the prism angle is. P 5.3.2.2 1 1 1 1 1 1 3 1 1 1 1 1 Cat. No. 471 830 471 050 662 093 471 090 460 250 460 010 460 040 460 320 460 353 460 351 441 530 300110 311 520 311 770 Description He-Ne laser , linearly polarized Fresnel’s mirror, adjustable Microscope slides 76 x 26 mm, 50 pcs. Fresnel biprism Prism table Lens f = +05 mm Lens f = + 200 mm Precision optical bench, standardized cross-section, 1 m Optics rider, H = 60 mm/W = 36 mm Optics rider, H = 60 mm/W = 50 mm Translucent screen Saddle base Vernier calipers, plastic Steel tape measure, 2 m 1 1 1 1 1 3 1 1 1 1 1 In each of these experiments, the respective wavelength Ö of the light used is determined by the distance d between two interference lines and the distance a of the (virtual) light sources. At a sufficiently great distance L between the (virtual) light sources and the projection screen, the relationship Ö=a· d L obtains. The determination of the quantity a depends on the respective experiment setup. P 5.3.2.1 P 5.3.2.2 P 5.3.2.3 182 P 5.3.2.3 1 1 1 1 1 1 3 1 1 1 1 1 P 5.3.2.1 Optics Wave optics P 5.3.3 Newton’s rings P 5.3.3.1 Newton’s rings in transmitted monochromatic light P 5.3.3.2 Newton’s rings in transmitted and reflected white light Newton’s rings in transmitted and reflected white light (P 5.3.3.2) Cat. No. 471 111 460 03 460 04 460 26 471 88 460 22 460 32 460 353 460 351 460 356 451 111 451 062 451 16 451 30 450 64 450 63 521 25 468 30 468 31 468 32 441 53 30011 501 33 Description Glass plates for Newton’s rings Lens f = + 100 mm Lens f = + 200 mm Iris diaphragm Beam divider Holder with spring clips Precision optical bench, standardized cross-section, 1 m Optics rider, H = 60 mm/W = 36 mm Optics rider, H = 60 mm/W = 50 mm Cantilever arm 100 Spectral lamp Na Spectral lamp Hg 100 Housing for spectral lamps Universal choke 230 V, 50 Hz Halogen lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Transformer 2 ... 12 V Mercury light filter, yellow Mercury light filter, green Mercury light filter, blue Translucent screen Saddle base Connecting lead, dia. 2.5 mm2, 100 cm, black 1 2 1 2 1 2 1 1 6 1 5 1 1 Newton’s rings are produced using an arrangement in which a convex lens with an extremely slight curvature is touching a glass plate, so that an air wedge with a spherically curved boundary surface is formed. When this configuration is illuminated with a vertically incident, parallel light beam, concentric interference rings (the Newton’s rings) are formed around the point of contact between the two glass surfaces both in reflection and in transmitted light. For the path difference of the interfering partial beams, the thickness d of the air wedge is the defining factor; this distance is not in a linear relation to the distance r from the point of contact: 2 d= r 2R R: bending radius of convex lens In the first experiment, the Newton’s rings are investigated with monochromatic, transmitted light. At a known wavelength Ö, the bending radius R is determined from the radii rn of the interference rings. Here, the relationship for constructive interference is: d=n· l where n = 0, 1, 2, ... 2 Thus, for the radii of the bright interference rings, we can say: r 2 = n · R · l where n = 0, 1, 2 , ... n In the second experiment, the Newton’s rings are studied both in reflection and in transmitted light. As the partial beams in the air wedge are shifted in phase by Ö/2 for each reflection at the glass surfaces, the interference conditions for reflection and transmitted light are complementary. The radii rn of the bright interference lines calculated for transmitted light using the equations above correspond precisely to the radii of the dark rings in reflection. In particular, the center of the Newton’s rings is bright in transmitted light and dark in reflection. As white light is used, the interference rings are bordered by colored fringes. 1 1 1 1 1 1 1 1 1 1 1 1 2 P 5.3.3.2 P 5.3.3.1 183 Wave optics P 5.3.4 Michelson interferometer Optics P 5.3.4.1 Setting up a Michelson interferometer on the laser optics base plate P 5.3.4.2 Determining the wavelength of the light of an He-Ne laser using a Michelson interferometer Setting up a Michelson interferometer on the laser optics base plate (P 5.3.4.1) In a Michelson interferometer, an optical element divides a coherent light beam into two parts. The component beams travel different paths, are reflected into each other and finally recombined. As the two component beams have a fixed phase relationship with respect to each other, interference patterns can occur when they are superposed on each other. A change in the optical path length of one component beam alters the phase relation, and thus the interference pattern as well. Thus, given a constant refractive index, a change in the interference pattern can be used to determine a change in the geometric path, e.g. changes in length due to heat expansion or the effects of electric or magnetic fields. When the geometric path is unchanged, then this configuration can be used to investigate changes in the refractive index due to variations e.g. in pressure, temperature and density. Cat. No. Description 473 400 471 830 0 473 411 473 420 473 432 473 430 473 460 473 470 473 480 441 530 300110 311 030 Laser optics base plate He-Ne laser 0.2/1 mW max, linearly polarized Laser mount Optics base Beam divider 50 % Holder for beam divider Planar mirror with fine adjustment Spherical lens, f + 2.7 mm Fine adjustment mechanism Translucent screen Saddle base Wooden ruler, 1 m long 1 1 1 4 1 1 2 1 1 1 1 In the second experiment, the wavelength of an He-Ne laser is determined from the change in the interference pattern when moving an interferometer mirror using the shifting distance Ws of the mirror. During this shift, the interference lines on the observation screen move. In evaluation, either the interference maxima or interference minima passing a fixed point on the screen while the plane mirror is shifted are counted. For the wavelength Ö, the following equation applies: In the first experiment, the Michelson interferometer is assembled on the vibration-proof laser optics base plate. This setup is ideal for demonstrating the effects of mechanical shocks and air streaking. 184 Ö=2· Ds Z Z: number of intensity maxima or minima counted P 5.3.4.2 1 1 1 5 1 1 2 1 1 1 1 1 P 5.3.4.1 Optics Wave optics P 5.3.5 Mach-Zehnderinterferometer P 5.3.5.1 Setting up a Mach-Zehnder interferometer on the laser optics base plate P 5.3.5.2 Measuring the refractive index of air with a Mach-Zehnder interferometer Measuring the refractive index of air with a Mach-Zehnder interferometer (P 5.3.5.2) Cat. No. 473 400 471 830 0 473 411 473 420 473 430 473 432 473 460 473 470 473 485 375 580 441 530 300110 311 030 300 020 666 555 Description Laser optics base plate He-Ne laser 0.2/1 mW max, linearly polarized Laser mount Optics base Holder for beam divider Beam divider 50 % Planar mirror with fine adjustment Spherical lens, f + 2.7 mm Evacuable chamber Hand vacuum and pressure pump Translucent screen Saddle base Wooden ruler, 1 m long Stand base, V-shape, 20 cm Universal clamp, 0 ... 80 mm dia. 1 1 1 5 2 2 2 1 1 1 1 P 5.3.5.2 1 1 1 6 2 2 2 1 1 1 1 1 1 1 1 Setting up a Mach-Zehnder interferometer on the laser optics base plate (P 5.3.5.1) In a Mach-Zehnder interferometer, an optical element divides a coherent light beam into two parts. The component beams are deflected by mirrors and finally recombined. As the two partial beams have a fixed phase relationship with respect to each other, interference patterns can occur when they are superposed on each other. A change in the optical path length of one component beam alters the phase relation, and consequently the interference pattern as well. As the component beams are not reflected into each other, but rather travel separate paths, these experiments are easier to comprehend and didactically more effective than experiments with the Michelson interferometer. However, the Mach-Zehnder interferometer is more difficult to adjust. P 5.3.5.1 In the first experiment, the Mach-Zehnder interferometer is assembled on the vibration-proof laser optics base plate. In the second experiment, the refractive index of air is determined. To achieve this, an evacuable chamber is placed in the path of one component beam of the Mach-Zehnder interferometer. Slowly evacuating the chamber alters the optical path length of the respective component beam. Setting up a Michelson interferometer is recommended before using a Mach-Zehnder interferometer for the first time. 185 Wave optics P 5.3.6 White-light reflection holography P 5.3.6.1 Creating white-light reflection holograms on the laser optics base plate Optics Creating white-light reflection holograms on the laser optics base plate (P 5.3.6.1) In creating white-light reflection holograms, a broadened laser beam passes through a film and illuminates an object placed behind the film. Light is reflected from the surface of the object back onto the film, where it is superposed with the light waves of the original laser beam. The film consists of a light-sensitive emulsion of sufficient thickness. Interference creates standing waves within the film, i. e. a series of numerous nodes and antinodes at a distance of Ö/4 apart. The film is exposed in the planes of the antinodes but not in the nodes. Semitransparent layers of metallic silver are formed at the exposed areas. Cat. No. Description 473 40 471 830 473 411 473 42 473 44 473 45 473 47 311 03 473 448 473 446 663 615 313 17 649 11 661 234 667 016 473 444 671 8910 672 4910 Laser optics base plate He-Ne laser 0.2/1 mW max, linearly polarized Laser mount Optics base Film holder Object holder Spherical lens f = 2.7 mm Wooden ruler, 1 m long Holography film Darkroom accessories Schuko socket strip, 5 sockets (safety mains sockets) Stopclock II, 60 s/30 min Set of 6 small trays, 1 x 1 RE Polyethylene bottle, 1000 ml, wn with screw cap Scissors, 200 mm, pointed Photographic chemicals Iron(III) nitrate nonahydrate, 250 g Potassium bromide (KBr), 100 g To reconstruct the image, the finished hologram is illuminated with white light – the laser is not required. The light waves reflected by the semitransparent layers are superposed on each other in such a way that they have the same properties as the waves originally reflected by the object. The observer sees a three-dimensional image of the object. Light beams originating at different layers only reinforce each other when they are in phase. The in-phase condition is only fulfilled for a certain wavelength, which allows the image to be reconstructed using white light. The object of this experiment is to create white-light reflection holograms. This process uses a protection class 2 laser, so as to minimize the risk of eye damage for the experimenter. Both amplitude and phase holograms can be created simply by varying the photochemical processing of the exposed film. Recommendation: the Michelson interferometer on the laser optics base plate is ideal for demonstrating the effects of disturbances due to mechanical shocks or air streaking in unsuitable rooms, which can prevent creation of satisfactory holograms. 186 P 5.3.6.1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 Optics Wave optics P 5.3.7 Transmission holography P 5.3.7.1 Creating transmission holograms on the laser optics base plate Creating transmission holograms on the laser optics base plate (P 5.3.7.1) Cat. No. 473 40 471 830 473 411 473 42 473 435 473 43 473 44 473 45 473 47 473 448 473 446 311 03 663 615 313 17 649 11 661 234 667 016 473 444 671 8910 672 4910 Description Laser optics base plate He-Ne laser 0.2/1 mW max, linearly polarized Laser mount Optics base Variable beam divider Holder for beam divider Film holder Object holder Spherical lens f = 2.7 mm Holography film Darkroom accessories Wooden ruler, 1 m long Schuko socket strip, 5 sockets (safety mains sockets) Stopclock II, 60 s/30 min Set of 6 small trays, 1 x 1 RE Polyethylene bottle, 1000 ml, wn with screw cap Scissors, 200 mm, pointed Photographic chemicals Iron(III) nitrate nonahydrate, 250 g Potassium bromide (KBr), 100 g 1 1 1 5 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 P 5.3.7.1 In creating transmission holograms, a laser beam is split into an object beam and a reference beam, and then broadened. The object beam illuminates an object and is reflected. The reflected light is focused onto a film together with the reference beam, which is coherent with the object beam. The film records an irregular interference pattern which shows no apparent similarity with the object in question. To reconstruct the hologram, a light beam which corresponds to the reference beam is diffracted at the amplitude hologram in such a way that the diffracted waves are practically identical to the object waves. In reconstructing a phase hologram the phase shift of the reference waves is exploited. In both cases, the observer sees a three-dimensional image of the object. The object of this experiment is to create transmission holograms and subsequently reconstruct them. This process uses a protection class 2 laser, so as to minimize the risk of eye damage for the experimenter. Both amplitude and phase holograms can be created simply by varying the photochemical processing of the exposed film. Recommendation: the Michelson interferometer on the laser optics base plate is ideal for demonstrating the effects of disturbances due to mechanical shocks or air streaking in unsuitable rooms, which can prevent creation of satisfactory holograms. 187 Polarization P 5.4.1 Basic experiments Optics P 5.4.1.1 Polarization of light through reflection at a glass plate P 5.4.1.2 Fresnel’s laws of reflection P 5.4.1.3 Polarization of light through scattering in an emulsion P 5.4.1.4 Malus’ law Fresnel’s laws of reflection (P 5.4.1.2) The fact that light can be polarized is important evidence of the transversal nature of light waves. Natural light is unpolarized. It consists of mutually independent, unordered waves, each of which has a specific polarization state. Polarization of light is the selection of waves having a specific polarization state. In the first experiment, unpolarized light is reflected at a glass surface. When we view this through an analyzer, we see that the reflected light as at least partially polarized. The greatest polarization is observed when reflection occurs at the polarizing angle (Brewster angle) ar. The relationship tanar = n gives us the refractive index n of the glass. Closer observation leads to Fresnel’s laws of reflection, which describe the ratio of reflected to incident amplitude for different directions of polarization. These laws are quantitatively verified in the second experiment. The third experiment demonstrates that unpolarized light can also be polarized through scattering in an emulsion, e. g. diluted milk, and that polarized light is not scattered uniformly in all directions. The aim of the fourth experiment is to derive Malus’s law: when linearly polarized light falls on an analyzer, the intensity of the transmitted light is I = I0 · cos2 G I0: intensity of incident light G: angle between direction of polarization and analyzer Cat. No. 477 20 460 25 450 64 450 63 450 66 521 25 450 60 450 51 460 20 521 210 Description Plate glass cell, 100 x 100 x 10 mm Prism table Halogen lamp housing W/100 W Halogen lampe, 12 V/100 W Picture slider for halogen lamp housing Transformer 2....12 V Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC / 30 W Iris diaphragm Polarization filter Lens, f = + 100 mm Lens, f = + 150 mm Lens, f = + 200 mm Translucent screen STE Photoelement Holder for plug-in elements Ammeter*, DC, I ≤ 1 mA, DI = 2 mA, Ri ≤ 50 V, e. g. Digital-analog multimeter METRAHit 24 S Small optical bench Swivel joint with angle scale Leybold multiclamp Stand base, V-shape, 28 cm Pair of cables, 1 m, red and blue Connecting lead, Ø 2.5 mm 2, 100 cm, black 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 460 26 472 401 460 03 460 08 460 04 441 53 578 62 460 21 531 281 460 43 460 40 301 01 300 01 501 46 501 33 1 2 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 5 2 2 1 6 2 1 2 2 6 1 1 * Readable in darkened room 188 P 5.4.1.4 1 2 1 1 1 1 6 1 1 2 P 5.4.1.2 P 5.4.1.3 P 5.4.1.1 Optics P 5.4.2 Birefringence Polarization P 5.4.2.1 Birefringence and polarization with calcite (Iceland spar) P 5.4.2.2 Quarter-wavelength and halfwavelength plate P 5.4.2.3 Photoelasticity: Investigating the distribution of strains in mechanically stressed bodies Quarter-wavelength and half-wavelength plate (P 5.4.2.2) Cat. No. 472 02 471 95 460 25 460 26 472 401 472 601 472 59 468 30 578 62 460 21 460 02 460 08 460 06 441 53 460 32 460 353 450 64 450 63 450 66 521 25 531 281 30011 501 46 Description Iceland spar crystal Set of photoelastic models Prism table Iris diaphragm Polarization filter Quarter-wavelength plate Half-wavelength plate Mercury light filter, yellow STE photoelement Holder for plug-in elements Lens f = + 50 mm Lens f = + 150 mm Lens f = – 100 mm Translucent screen Precision optical bench, standardized cross-section, 1 m Optics rider, H = 60 mm/W = 36 mm Halogen lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Picture slider for halogen lamp housing Transformer 2 ... 12 V Ammeter, DC, I ≤ 1 mA, W I = 2 BA, Ri ≤ 50 E e. g. Digital-analog multimeter METRAHit 24 S Saddle base Pair of cables, 100 cm, red and blue 1 1 1 1 2 2 2 1 1 1 1 1 2 1 1 1 7 1 1 1 1 1 1 7 1 1 1 1 1 1 1 2 1 1 1 9 1 1 1 1 1 1 2 2 The validity of Snell’s law of refraction is based on the premise that light propagates in the refracting medium at the same velocity in all directions. In birefringent media, this condition is only fulfilled for the ordinary component of the light beam (the ordinary ray); the law of refraction does not apply for the extraordinary ray. The first experiment looks at birefringence of calcite (Iceland spar). We can observe that the two component rays formed in the crystal are linearly polarized, and that the directions of polarization are perpendicular to each other. The second experiment investigates the properties of Ö/4 and Ö/2 plates and explains these in terms of their birefringence; it further demonstrates that the names for these plates refer to the path difference between the ordinary and the extraordinary rays through the plates. In the third experiment, the magnitude and direction of mechanical stresses in transparent plastic models are determined. The plastic models become optically birefringent when subjected to mechanical stress. Thus, the stresses in the models can be revealed using polarization-optical methods. For example, the plastic models are illuminated in a setup consisting of a polarizer and analyzer arranged at right angles. The stressed points in the plastic models polarize the light elliptically. Thus, the stressed points appear as bright spots in the field of view. In another configuration, the plastic models are illuminated with circularly polarized light and observed using a quarter-wavelength plate and an analyzer. Here too, the stressed points appear as bright spots in the field of view. P 5.4.2.2 P 5.4.2.3 P 5.4.2.1 Photoelasticity: Investigating the distribution of strains in mechanically stressed bodies (P 5.4.2.3) 189 Polarization P 5.4.3 Optical activity, polarimetry P 5.4.3.1 Rotation of the plane of polarization with quartz P 5.4.3.2 Rotation of the plane of polarization with sugar solutions P 5.4.3.3 Building a half-shadow polarimeter with discrete elements P 5.4.3.4 Determining the concentration of sugar solutions with a standard commercial polarimeter Optics Rotation of the plane of polarization with sugar solutions (P 5.4.3.2) Optical activity is the property of some substances of rotating the plane of linearly polarized light as it passes through the material. The angle of optical rotation is measured using a device called a polarimeter. The first experiment studies the optical activity of crystals, in this case a quartz crystal. Depending on the direction of intersection with respect to the optical axis, the quartz rotates the light clockwise (“right-handed”), counterclockwise (“left-handed”) or is optically inactive. The angle of optical rotation is closely dependent on the wavelength of the light; therefore a yellow filter is used. The second experiment investigates the optical activity of a sugar solution. For a given cuvette length d, the angles of optical rotation R of optically active solutions are proportional to the concentration c of the solution. a = [a] · c · d [a]: rotational effect of the optically active solution The object of the third experiment is to assemble a half-shadow polarimeter from discrete components. The two main elements are a polarizer and an analyzer, between which the optically active substance is placed. Half the field of view is covered by an additional, polarizing foil, of which the direction of polarization is rotated slightly with respect to the first. This facilitates measuring the angle of optical rotation. In the fourth experiment, the concentrations of sugar solutions are measured using a standard commercial polarimeter and compared with the values determined by weighing. P 5.4.3.2 P 5.4.3.3 Cat. No. Description 472 62 472 64 472 65 460 22 450 64 450 63 450 66 521 25 468 30 468 03 468 07 468 11 472 401 463 80 111 Quartz, parallel Quartz, right-handed Quartz, left-handed Holder with spring clips Halogen lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Picture slider for halogen lamp housing Transformer 2 ... 12 V Mercury light filter, yellow Monochromatic light filter, red Monochromatic light filter, yellow-green Monochromatic light filter, blue with violet Polarization filters Slide cover slip 5 x 5 cm 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 460 03 477 20 477 25 520 511 08 674 6050 460 25 441 53 460 43 301 01 300 01 657 590 664111 666 963 Lens f = + 100 mm Plate glass cell, 100 x 100 x 10 mm Plate glass cell, 100 x 80 x 25 mm Polarization film D(+)-saccharose, 100 g Prism table Translucent screen Small optical bench Leybold multiclamp Stand base, V-shape, 28 mm Polarimeter P1000 Beaker 100 ml, ts, hard glass Spatula with spoon end, 120 x 20 mm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 6 1 7 1 1 1 1 1 Determining the concentration of sugar solutions with a standard commercial polarimeter (P 5.4.3.4) 667 793 501 33 Electronic balance LS 200, 200 g : 0.1 g Connecting lead, dia. 2.5 mm2, 100 cm, black 2 2 2 190 P 5.4.3.4 1 P 5.4.3.1 1 Optics P 5.4.4 Kerr effect Polarization P 5.4.4.1 Investigating the Kerr effect in nitrobenzol Investigating the Kerr effect in nitrobenzol (P 5.4.4.1) Cat. No. 473 31 673 9410 521 70 501 05 450 64 450 63 521 25 450 66 468 03 468 05 468 07 468 11 472 401 460 03 460 25 441 53 460 32 460 351 501 33 Description Kerr cell Nitrobenzol High voltage power supply 10 kV High voltage cables Lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Transformer 2 ... 12 V Picture slider for halogen lamp housing Monochromatic light filter, red Monochromatic light filter, yellow Monochromatic light filter, yellow-green Monochromatic light filter, blue with violet Polarization filter Lens f = + 100 mm Prism table Translucent screen Precision optical bench, standardized cross-section, 1 m Optics rider H = 60 mm/W = 50 mm Connecting lead, dia. 2.5 mm2, 100 cm, black 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 6 2 In 1875, J. Kerr discovered that electrical fields cause birefringence in isotropic substances. The birefringence increases quadratically with the electric field strength. For reasons of symmetry, the optical axis of birefringence lies in the direction of the electric field. The normal refractive index of the substance is changed to ne for the direction of oscillation parallel to the applied field, and to no for the direction of oscillation perpendicular to it. The experiment results in the relationship ne – no = K · Ö · E2 K: Kerr constant, l: wavelength of light used, E: electric field strength The experiment demonstrates the Kerr effect for nitrobenzol, as the Kerr constant is particularly great for this material. The liquid is filled into a small glass vessel in which a suitable plate capacitor is mounted. The arrangement is placed between two polarization filters arranged at right angles, and illuminated with a linearly polarized light beam. The field of view is dark when no electric field is applied. When an electric field is applied, the field of view brightens, as the light beam is elliptically polarized when passing through the birefringent liquid. P 5.4.4.1 191 Polarization P 5.4.5 Pockels effect Optics P 5.4.5.1 Demonstrating the Pockels effect in a conoscopic beam path P 5.4.5.2 Pockels effect: transmitting information using modulated light Demonstrating the Pockels effect in a conoscopic beam path (P 5.4.5.1) The occurrence of birefringence and the alteration of existing birefringence in an electrical field as a linear function of the electric field strength is known as the Pockels effect. In terms of the visible phenomena, it is related to the Kerr effect. However, due to its linear dependency on the electric field strength, the Pockels effect can only occur in crystals without an inversion center, for reasons of symmetry. The first experiment demonstrates the Pockels effect in a lithium niobate crystal placed in a conoscopic beam path. The crystal is illuminated with a divergent, linearly polarized light beam, and the transmitted light is viewed behind a perpendicular analyzer. The optical axis of the crystal, which is birefringent even when no electric field is applied, is parallel to the incident and exit surfaces; as a result, the interference pattern consists of two sets of hyperbolas which are rotated 90h with respect to each other. The bright lines of the interference pattern are due to light rays for which the difference W between the optical paths of the extraordinary and ordinary rays is an integral multiple of the wavelength Ö. The Pockels effect alters the difference of the main refractive indices, no – ne, and consequently the position of the interference lines. When the so-called half-wave voltage UÖ is applied, W changes by one half wavelength. The dark interference lines move to the position of the bright lines, and vice versa. The process is repeated each time the voltage is increased by UÖ. The second experiment shows how the Pockels cell can be used to transmit audio-frequency signals. The output signal of a function generator with an amplitude of several volts is superposed on a DC voltage which is applied to the crystal of the Pockels cell. The intensity of the light transmitted by the Pockels cell is modulated by the superposed frequency. The received signal is output to a speaker via an amplifier and thus made audible. Cat. No. Description 472 90 521 70 471 830 460 01 460 02 472 401 460 32 460 353 441 53 522 56 578 62 460 21 522 61 587 08 30011 500 604 500 621 500 641 500 642 501 46 500 98 Pockels cell High voltage power supply 10 kV He-Ne laser 0.2/1 mW max, linearly polarized Lens f = + 5 mm Lens f = + 50 mm Polarization filter Precision optical bench, standardized cross-section, 1 m Optics rider, H = 60 mm/W = 36 mm Translucent screen Function generator P, 100 mHz to 100 kHz STE photoelement Holder for plug-in elements AC/DC-amplifier Broad-band speaker Saddle base Safety connection leads, 10 cm, black Safety connection leads, 50 cm, red Safety connection leads, 100 cm, red Safety connection leads, 100 cm, blue Pair of cables, 100 cm, red and blue 1 1 1 1 1 1 1 5 1 1 1 1 1 I Set 6 safety adapter sockets, black I I 192 P 5.4.5.2 1 1 1 1 1 4 1 1 1 1 1 1 2 1 1 2 1 P 5.4.5.1 Optics Polarization P 5.4.6 Faraday effect P 5.4.6.1 Faraday effect: determining Verdet’s constant for flint glass as a function of the wavelength Faraday effect: determining Verdet’s constant for flint glass as a function of the wavelength (P 5.4.6.1) Cat. No. 560 481 460 358 562 11 560 31 562 13 450 63 450 64 450 66 468 05 468 09 468 11 468 13 460 02 472 401 460 32 460 351 441 53 521 25 521 39 531 281 516 60 516 62 501 16 300 02 300 41 301 01 501 45 501 46 501 461 Description Flint glass square with holder Rider base with threads U-core with yoke Pair of bored pole pieces Coil with 250 turns Halogen lamp, 12 V/100 W Halogen lamp housing 12 V, 50/100W Picture slider for halogen lamp housing Monochromatic light filter, yellow Monochromatic light filter, blue-green Monochromatic light filter, blue with violet Monochromatic light filter, violet Lens f = + 50 mm Polarization filter Precision optical bench, standardized profile, 1 m Optics rider, H = 60 mm/W = 50 mm Translucent screen Transformer 2 ... 12 V Variable extralow voltage transformer Ammeter, DC, I ≤ 10 A, W I = 0,2 A, e. g. Digital-analog multimeter METRAHit 24 S Tangential B-probe Teslameter Multicore cable, 6-pole, 1.5 m long Stand base, V-shape, 20 cm Stand rod, 25 cm Leybold multiclamp Pair of cables, 50 cm, red and blue Pair of cables, 100 cm, red and blue Pair of cables, 100 cm, black 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 Transparent isotropic materials become optically active in a magnetic field; in other words, the plane of polarization of linearly polarized light rotates when passing through the material. M. Faraday discovered this effect in 1845 while seeking a relationship between magnetic and optical phenomena. The angle of optical rotation of the plane of polarization is proportional to the illuminated length s and the magnetic field B. Df = V · B · s The proportionality constant V is known as Verdet’s constant, and depends on the wavelength Ö of the light and the dispersion. e · Ö · dn V= dÖ 2mc2 For flint glass, the following equation approximately obtains: dn 1,8 · 10–14 m2 = dÖ Ö3 In this experiment, the magnetic field is initially calibrated with reference to the current through the electromagnets using a teslameter, and then the Faraday effect in a flint glass square is investigated. To improve measuring accuracy, the magnetic field is reversed each time and twice the angle of optical rotation is measured. The proportionality between the angle of optical rotation and the magnetic field and the decrease of Verdet’s constant with the wavelength Ö are verified. P 5.4.6.1 193 Light Intensity P 5.5.1 Quantities and measuring methods of lighting engineering P 5.5.1.1 Determining the radiant flux density and the luminous intensity of a halogen lamp P 5.5.1.2 Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY P 5.5.1.3 Verifying Lambert’s law of radiation Optics Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY (P 5.5.1.2 a) There are two types of physical quantities used to characterize the brightness of light sources: quantities which refer to the physics of radiation, which describe the energy radiation in terms of measurements, and quantities related to lighting engineering, which describe the subjectively perceived brightness under consideration of the spectral sensitivity of the human eye. The first group includes the irradiance Ee, which is the radiated power per unit of area Fe. The corresponding unit of measure is watts per square meter. The comparable quantity in lighting engineering is illuminance E, i. e. the emitted luminous flux per unit of area F, and it is measured in lumens per square meter, or lux for short. In the first experiment, the irradiance is measured using the Moll’s thermopile, and the luminous flux is measured using a luxmeter. The luxmeter is matched to the spectral sensitivity of the human eye V (Ö) by means of a filter placed in front of the photoelement. A halogen lamp serves as the light source. From its spectrum, most of the visible light is screened out using a color filter; subsequently, a heat filter is used to absorb the infrared component of the radiation. The second experiment demonstrates that the luminous intensity is proportional to the square of the distance between a point-type light source and the illuminated surface. The aim of the third experiment is to investigate the angular distribution of the reflected radiation from a diffusely reflecting surface, e.g. matte white paper. To the observer, the surface appears uniformly bright; however, the apparent surface area varies with the cos of the viewing angle. The dependency of the luminous intensity is described by Lambert’s law of radiation: Ee (F) = Ee (0) · cos F P 5.5.1.2 (b) 1 1 1 1 1 1 1 1 1 1 2 1 2 1 P 5.5.1.2 (a) Cat. No. Description 450 64 450 63 450 68 521 25 450 66 450 60 450 51 521 210 Halogen lamp housing 12 V, 50/100 W Halogen lamp, 12 V/100 W Halogen lamp, 12 V/50 W Transformer 2 ... 12 V Picture slider for halogen lamp housing Lamp housing Lamp, 6 V/30 W Transformer, 6 V AC, 12 V AC/30 VA Monochromatic light filter, red Iris diaphragm Lens f = + 100 mm Holder with spring clips Moll’s thermopile Microvoltmeter Sensor CASSY Lux sensor Lux box CASSY Lab Hand-held Lux-UV-IR-Meter Small optical bench Swivel joint with angle scale Insulated stand rod, 25 cm long Small clip plug Leybold multiclamp Stand base, V-shape, 20 cm Stand base, V-shape, 28 cm Pair of cables, 100 cm, red and blue Connecting leads, dia. 2.5 mm2, 100 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 468 03 460 26 460 03 460 22 557 36 532 13 524 010 666 243 524 051 524 200 666 230 460 43 460 40 59013 590 02 301 01 300 02 300 01 501 46 501 33 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 1 2 1 194 P 5.5.1.3 1 1 1 1 1 1 1 1 1 2 1 4 2 1 2 P 5.5.1.1 Optics Light Intensity P 5.5.2 Laws of radiation P 5.5.2.1 Stefan-Boltzmann law: measuring the radiant intensity of a “black body” as a function of temperature P 5.5.2.2 Stefan-Boltzmann law: measuring the radiant intensity of a “black body” as a function of temperature – Recording and evaluating with CASSY P 5.5.2.3 Confirming the laws of radiation with Leslie’s tube Stefan-Boltzmann law: measuring the radiant intensity of a “black body” as a function of temperature (P 5.5.2.1) Cat. No. 389 43 555 81 555 84 502 061 389 26 389 28 666 190 666 193 557 36 532 13 524 010 524 045 524 040 524 200 460 43 300 01 301 01 666 555 303 25 590 06 665 009 388 181 521 230 Description Black body accessory Electric oven, 230 V Support for electric oven Safety connection box with ground Leslie’s cube Stirrer for Leslie’s cube Digital thermometer with one input Temperature sensor NiCr-Ni Moll’s thermopile Microvoltmeter Sensor CASSY Temperature box (NiCrNi/NTC) mV-Box CASSY Lab Small optical bench Stand base, V-shape, 28 cm Leybold multiclamp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 4 1 3 1 1 1 Universal clamp, 0 ... 80 mm dia. Immersion heater Plastic beaker, 1000 ml Funnel, dia. 75 mm, plastic Submersible pump, 12 V Low voltage power supply Silicone tubing, i.d. 7 x 1.5 mm, 1 m Pair of cables, 100 cm, red and blue additionally required: PC with Windows 95/NT or higher * additionally recommended 1* 1* 1* 1 1* 1* 1* 1 1 1 667194 501 46 The total radiated power MB of a black body increases in proportion to the fourth power of its absolute temperature T (StefanBoltzmann’s law). MB = s · T 4 s = 5.67 · 10–8 W m–2 K–4: (Stefan-Boltzmann’s constant) For all other bodies, the radiated power M is less than that of the black body, and depends on the properties of the surface of the body. The emittance of the body is described by the relationship e= M MB M: radiated power of body In the first two experiments, a cylindrical electric oven with a burnished brass cylinder is used as a “black body”. The brass cylinder is heated in the oven to the desired temperature between 300 and 750 K. A thermocouple is used to measure the temperature. A water-coolable screen is positioned in front of the oven to ensure that the setup essentially measures only the temperature of the burnished brass cylinder. The measurement is conducted using a Moll’s thermopile; its output voltage provides a relative measure of the radiated power M. The thermopile can be connected either to an amplifier or, via the amplifier box, to the CASSY computer interface device. In the former case, the measurement must by carried out manually, point by point; the latter configuration enables computer-assisted measuring and evaluation. The aim of the evaluation is to confirm Stefan-Boltzmann’s law. The third experiment uses a radiation cube after Leslie (“Leslie’s cube”). This cube has four different face surfaces (metallic matte, metallic shiny, black finish and white finish), which can be heated from the inside to almost 100 hC by filling the cube with boiling water. The heat radiated by each of the surfaces is measured as a function of the falling temperature. The aim of the evaluation is to compare the emittances of the cube faces. P 5.5.2.2 P 5.5.2.3 P 5.5.2.1 195 Velocity of light P 5.6.1 Measurement according to Foucault/Michelson P 5.6.1.1 Determining the velocity of light by means of the rotating-mirror method according to Foucault and Michelson – measuring the image shift as a function of the rotational speed of the mirror P 5.6.1.2 Determining the velocity of light by means of the rotating-mirror method according to Foucault and Michelson – measuring the image shift for the maximum rotational speed of the mirror Optics Determining the velocity of light by means of the rotating-mirror method according to Foucault and Michelson – measuring the image shift as a function of the rotational speed of the mirror (P 5.6.1.1) Measurement of the velocity of light by means of the rotary mirror method utilizes a concept first proposed by L. Foucault in 1850 and perfected by A. A. Michelson in 1878. In the variation utilized here, a laser beam is deviated into a fixed end mirror located next to the light source via a rotating mirror set up at a distance of a = 12.1 m. The end mirror reflects the light so that it returns along the same path when the rotary mirror is at rest. Part of the returning light is imaged on a scale using a beam divider. A lens with f = 5 m images the light source on the end mirror and focuses the image of the light source from the mirror on the scale. The main beam between the lens and the end mirror is parallel to the axis of the lens, as the rotary mirror is set up in the focal point of the lens. Once the rotary mirror is turning at a high frequency O, the shift DO of the image on the scale is observed. In the period Dt = 2a , c which the light requires to travel to the rotary mirror and back to the end mirror, the rotary mirror turns by the angle Da = 2 S v · Dt Thus, the image shift is Dx = 2Da · a The velocity of light can then be calculated as c = 8p · a2 · n Dx To determine the velocity of light, it is sufficient to measure the shift in the image at the maximum speed of the mirror, which is known. Measuring the image shift as a function of the speed supplies more precise results. Cat. No. 476 40 471 830 463 20 460 12 471 88 460 22 311 09 521 40 575 211 559 92 501 02 501 10 300 44 300 42 300 41 300 01 300 02 300 11 301 01 301 09 311 03 537 36 537 35 502 05 504 48 500 644 Description Rotary mirror for determination of the velocity of light He-Ne laser 0.2/1 mW max., linearly polarized Front silvered mirror Lens, f = approx. + 5 m Beam splitter Holder with spring clips Glass scale, 5 cm long Variable low voltage transformer 0....250 V Two-channel oscilloscope 303 Semiconductor detector BNC cable, 1 m long Straight BNC Stand rod, 100 cm Stand rod, 47 cm Stand rod, 25 cm Stand base, V-shape, 28 cm Stand base, V-shape, 20 cm Saddle base Leybold multiclamp Bosshead S Wooden ruler, 1 m long Rheostat 1000 V Rheostat 330 V Measuring junction box Two-way switch Safety connection lead, 100 cm, black 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 2 1 1 196 P 5.6.1.2 1 1 1 1 1 1 1 1 1 1 4 2 1 1 1 1 1 5 P 5.6.1.1 Optics Velocity of light P 5.6.2 Measuring with short light pulses P 5.6.2.1 Determining the velocity of light in air from the path and transit time of a short light pulse P 5.6.2.2 Determining the propagation velocity of voltage pulses in coaxial cables Determining the velocity of light in air from the path and transit time of a short light pulse (not shown: mirror T1) (P 5.6.2.1) Cat. No. 476 50 Description Light velocity measuring instrument 1 1 460 10 460 32 460 352 575 211 501 02 501 024 501 091 501 10 575 35 577 79 577 28 311 03 300 01 300 44 301 01 300 11 Lens, f = + 200 mm Precision optical bench, standardized cross section, 1 m Optics rider, H = 90 mm/W = 50 mm Two-channel oscilloscope 303 BNC cable, 1 m long BNC cable, 10 m long T-adapter BNC Straight BNC BNC/4 mm adapter, 2-pole STE regulation resistor 1 kV STE resistor 47 V, 2 W Wooden ruler, 1 m long Stand base, V-shape, 28 cm Stand rod, 100 cm Leybold multiclamp Saddle base 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 Schematic diagram of light velocity measurement with short light pulses The light velocity measuring instrument emits pulses of light with a pulse width of about 20 ns. After traversing a known measuring distance in both directions, the light pulses are converted into voltage pulses for observation on the oscilloscope. In the first experiment, the path of the light pulses is varied once, and the change in the transit time is measured with the oscilloscope. The velocity of light can then be calculated as quotient of the change in the transit distance and the change in the transit time. Alternatively, the total transit time of the light pulses can be measured in absolute terms using a reference pulse. In this case, the velocity of light can be calculated as quotient of the transit distance and the transit time. A quartz-controlled oscilloscope signal can be displayed on the instrument simultaneously with the measuring pulse in order to calibrate timing. Time measurement is then independent of the time base of the oscilloscope. In the second experiment, the propagation velocity of voltage pulses in coaxial cables is determined. In this configuration, the reference pulses of the light velocity measuring instrument are output to an oscilloscope and additionally fed into a 10 m long coaxial cable via a T-connector. After reflection at the cable end, the pulses return to the oscilloscope, delayed by the transit time. The propagation velocity n can be calculated from the double cable length and the time difference between the direct and reflected voltage pulses. By inserting these values in the equation n= c c: velocity of light in a vacuum öää er we obtain the relative dielectricity er of the insulator between the inner and outer conductors of the coaxial cable. By using a variable terminating resistor R at the cable end, it becomes possible to additionally measure the reflection behavior of voltage pulses, In particular, the special cases “open cable end” (no phase shift at reflection), “shorted cable end” (phase shift due to reflection) and “termination of cable end with the 50 Ö characteristic wave impedance” (no reflection) are of special interest here. P 5.6.2.2 P 5.6.2.1 197 Velocity of light P 5.6.3 Measuring with a periodical light signal P 5.6.3.1 Determining the velocity of light using a periodical light signal and a short measuring distance P 5.6.3.2 Determining the velocity of light for different propagation media Optics Determining the velocity of light using a periodical light signal and a short measuring distance (P 5.6.3.1) In determining the velocity of light with an electronically modulated signal, a light emitting diode which pulses at a frequency of 60 MHz is used as the light transmitter. The receiver is a photodiode which converts the light signal into a 60 MHz AC voltage. A connecting lead transmits a reference signal to the receiver which is synchronized with the transmitted signal and in phase with it at the start of the measurement. The receiver is then moved by the measuring distance ∆s, so that the received signal is phase-shifted by the additional transit time ∆ t of the light signal. Df = 2S · f1 · Dt where f1 = 60 MHz Alternatively, a medium with a greater index of refraction can be placed in the beam path. The apparent transit time to be measured is increased by means of an electronic “trick”. The received signal and the reference signal are each mixed (multiplied) with a 59.9 MHz signal before being fed through a frequency filter which only passes the lowfrequency components with the differential frequency f1 – f2 = 0.1 MHz. This mixing has no effect on the phase shift; however, this phase shift is now for a transit time ∆ t’ increased by a factor of f1 = 600 f1 – f2 In the first experiment, the apparent transit time ∆ t’ is measured as a function of the measuring distance ∆s, and the velocity of light in the air is calculated according to the formula Ds · f1 c= Dt’ f1 – f2 The second experiment determines the velocity of light in various propagation media. In the way of accessories, this experiment requires a tube 1 m long with two end windows, suitable for filling with water, a glass cell 5 cm wide for other liquids and an acrylic glass body 5 cm wide. To enable more precise determinations of the velocity of light, it is recommended that the frequencies f1 and f1 – f2 be measured using a digital counter. P 5.6.3.2 (b) 1 1 1 1 1 1 1 1* 3 1 P 5.6.3.2 (a) Cat. No. Description 476 30 476 35 671 9720 672 1210 477 03 476 34 460 25 460 08 575 221 575 48 30011 311 02 Light transmitter and receiver Tube with 2 end windows Ethanol, completely denaturated, 1 l Glycerine, 99 %, 250 ml Plate glass cell, 50 x 50 x 50 mm Acrylic glass block Prism table Lens, f = + 150 mm Two-channel oscilloscope 1004 Digital Counter Saddle base Vertical scale, 1 m long *additionally recommended 1 1 1 1 1 1* 2 1 1 1 1* 4 1 Block circuit diagram 198 P 5.6.3.2 (c) 1 1 1 1 1 1* 3 1 P 5.6.3.1 Optics Spectrometer P 5.7.1 Prism spectrometer P 5.7.1.1 Measuring the line spectra of inert gases and metal vapors using a prism spectrometer Measuring the line spectra of inert gases and metal vapors using a prism spectrometer (P 5.7.1.1) Cat. No. 467 23 451 031 451 041 451 011 451 071 451 081 451 111 451 16 451 30 521 210 Description Spectrometer and goniometer Spectral lamp He Spectral lamp Cd Spectral lamp Ne Spectral lamp Hg/Cd Spectral lamp TI Spectral lamp Na Housing for spectrum lamps Universal choke, in housing, 230 V, 50 Hz Transformer, 6 V~, 12 V~/ 30 W Stand base, V-shape, 20 cm * additionally recommended 1 1 1 1* 1* 1* 1* 1 1 1 1 300 02 To assemble the prism spectrometer, a flint glass prism is placed on the prism table of a goniometer. The light of the light source to be studied passes divergently through a collimator and is incident on the prism as a parallel light beam. The arrangement exploits the wavelength-dependency of the refractive index of the prism glass: the light is refracted and each wavelength is deviated by a different angle. The deviated beams are observed using a telescope focused on infinity which is mounted on a slewable arm; this allows the position of the telescope to be determined to within a minute of arc. The refractive index is not linearly dependent on the wavelength; thus, the spectrometer must be calibrated. This is done using e.g. an He spectral lamp, as its spectral lines are known and distributed over the entire visible range. In this experiment, the spectrometer is used to observe the spectral lines of inert gases and metal vapors which have been excited to luminance. To identify the initially “unknown” spectral lines, the angles of deviation are measured and then converted to the corresponding wavelength using the calibration curve. P 5.7.1.1 Ray path in a prism spectrometer Note: as an alternative to the prism spectrometer, the goniometer can also be used to set up a grating spectrometer (see P 5.7.2.1) 199 Spectrometer P 5.7.2 Grating spectrometer Optics P 5.7.2.1 Measuring the line spectra of inert gases and metal vapors using a grating spectrometer Measuring the line spectra of inert gases and metal vapors using a grating spectrometer (P 5.7.2.1) To create a grating spectrometer, a copy of a Rowland grating is mounted on the prism table of the goniometer in place of the prism. The ray path in the grating spectrometer is essentially analogous to that of the prism spectrometer (see P 5.7.1.1). However, in this configuration the deviation of the rays by the grating is proportional to the wavelength: sinDa = n · g · Ö n: diffraction order, g: grating constant, l: wavelength, Da: angle of deviation of nth-order spectral line Consequently, the wavelengths of the observed spectral lines can be calculated directly from the measured angles of deviation. In this experiment, the grating spectrometer is used to observe the spectral lines of inert gases and metal vapors which have been excited to luminance. To identify the initially “unknown” spectral lines, the angles of deviation are measured and then converted to the corresponding wavelength. The resolution of the grating spectrometer is sufficient to determine the distance between the two yellow sodium D-lines Ö(D1) – Ö(D2) = 0.60 nm with an accuracy of 0.10 nm. However, this high resolution is achieved at the cost of a loss of intensity, as a significant part of the radiation is lost in the undiffracted zero order and the rest is distributed over multiple diffraction orders on both sides of the zero order. Cat. No. 467 23 471 23 451 031 451 111 451 011 451 041 451 071 451 081 451 16 451 30 521 210 Description Spectrometer and goniometer Copy of a Rowland grating, 6000 lines/cm approx. Spectral lamp He, pin contact Spectral lamp Na, pin contact Spectral lamp Ne, pin contact Spectral lamp Cd, pin contact Spectral lamp Hg/Cd, pin contact Spectral lamp TI, pin contact Housing for spectrum lamps w. pin socket Universal choke, in housing, 230 V, 50 Hz Transformer, 6 V~, 12 V~/ 30 W Stand base, V-shape, 20 cm * additionally recommended 1 1 1 1 1* 1* 1* 1* 1 1 1 1 300 02 Ray path in a grating spectrometer 200 P 5.7.2.1 Optics Spectrometer P 5.7.2 Grating spectrometer P 5.7.2.2 Assembling a grating spectrometer for measuring transmission curves Assembling a grating spectrometer for measuring transmission curves (P 5.7.2.2) Cat. No. Description 337 47 VideoCom 1 1 460 32 460 34 471 23 460 14 460 08 460 22 460 356 460 351 450 60 450 51 460 20 521 210 Precision optical bench, standardized cross section, 1 m Auxiliary bench with swivel joint Copy of a Rowland grating, 6000 lines/cm approx. Adjustable slit Lens, f = + 150 mm Holder with spring clips Cantilever arm 100 mm Optics rider, H = 60 mm/W = 50 mm Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC, 12 V AC/ 30 W Filter set red, green, blue Filter set yellow, cyan, magenta Monochromatic light filter, red Monochromatic light filter, yellow Monochromatic light filter, yellow/green Monochromatic light filter, blue-green additionally required: PC with Windows 95/NT or higher * additionally recommended 2 1 1 1 1 1 5 1 1 1 1 1 1 1* 1* 1* 1* 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1* 1* 1* 1* 1 467 95 467 96 468 03 468 05 468 07 468 09 When used in conjunction with a grating spectrometer, the single-line CCD camera VideoCom is ideal for relative measurements of spectral intensity distributions. In such measurements, each pixel of the CCD camera is assigned a wavelength Ö = d · sin R in the first diffraction order of the grating. The spectrometer is assembled on the optical bench using individual components. The grating in this experiment is a copy of a Rowland grating with approx. 6000 lines /cm. The diffraction pattern behind the grating is observed with VideoCom. The VideoCom software makes possible comparison of two intensity distributions, and thus recording of transmission curves of color filters or other light-permeable bodies. The spectral intensity distribution of a light source is measured both with and without filter, and the ratio of the two measurements is graphed as a function of the wavelength. This experiment records the transmission curves of color filters. It is revealed that simple filters are permeable for a very broad wavelength range within the visible spectrum of light, while socalled line filters have a very narrow permeability range. P 5.7.2.2 (a) P 5.7.2.2 (b) Transmissions curves of various color filters 201 Atomic and nuclear physics Table of contents Atomic and nuclear physics P6 Atomic and nuclear physics P 6.1 P 6.1.1 P 6.1.2 P 6.1.3 P 6.1.4 P 6.1.5 P 6.1.6 Introductory experiments Oil-spot experiment Millikan experiment Specific electron charge Planck's constant Dualism of wave and particle Paul trap 205 206 207 208–209 210 211 P 6.4 P 6.4.1 P 6.4.2 P 6.4.3 P 6.4.4 Radioactivity Detection of radioactivity Poisson distribution Radioactive decay and half-life Attenuation of R, T and H radiation 225 226 227 228 P 6.5 P 6.5.1 P 6.5.2 P 6.5.3 P 6.5.4 P 6.5.5 P 6.5.6 Nuclear physics Demonstration of particle tracks Rutherford scattering Nuclear magnetic resonance (NMR) R spectroscopy H spectroscopy Compton effect 229 230 231 232 233 234 P 6.2 P 6.2.1 P 6.2.2 P 6.2.3 P 6.2.4 P 6.2.5 P 6.2.6 P 6.2.7 P 6.2.8 Atomic shell The Balmer series of hydrogen Emission and absorption spectra Inelastic electron collisions Franck-Hertz experiment Critical potential Electron spin resonance (ESR) Normal Zeeman effect Optical pumping (anomalous Zeeman effect) 212 213 214 215–216 217 218 219 220 P 6.3 P 6.3.1 P 6.3.2 P 6.3.3 P 6.3.4 X-rays Demonstrating x-rays Attenuation of x-rays Physics of the atomic shell X-ray physics with the x-ray apparatus P 221 222 223 224 204 Atomic and nuclear physics Introductory experiments P 6.1.1 Oil-spot experiment P 6.1.1.1 Determining the size of oil molecules Determining the size of oil molecules (P 6.1.1.1) Cat. No. 664 179 665 844 664 110 665 751 665 754 300 02 300 43 301 01 666 555 Description Crystallization dish, 230 mm dia., 100 mm high Burette, 10 ml: 0.05, w. lateral stopcock, amber glass, Schellbach blue line Beaker, 50 ml, ss, hard glass Graduated cylinder, 10 ml: 0.2 Graduated cylinder, 100 ml: 1 Stand base, V-shape, 20 cm Stand rod, 75 cm Leybold multiclamp Universal clamp, 0...80 mm 1 1 1 1 1 1 1 1 1 1 1 1 One important issue in atomic physics is the size of the atom. An investigation of the size of molecules makes it easier to come to a usable order of magnitude by experimental means. This is estimated from the size of an oil spot on the surface of water using simple means. In this experiment, a drop of glycerin nitrioleate as added to a grease-free water surface dusted with Lycopodium spores. Assuming that the resulting oil spot has a thickness of one molecule, we can calculate the size d of the molecule according to V d= A from the volume V of the oil droplet and the area A of the oil spot. The volume of the oil spot is determined from the number of drops needed to fill a volume of 1 cm3. The area of the oil spot is determined using graph paper. 675 3410 Water, pure, 5 l 672 1240 Glycerin trioleate, 100 ml 674 2220 Benzine, 40–70°C Determining the area A of the oil spot P 6.1.1.1 205 Introductory experiments P 6.1.2 Millikan experiment Atomic and nuclear physics P 6.1.2.1 Determining the electrical charge of the electron after Millikan and demonstrating the quantum nature of the charge – measuring the suspension voltage and the falling speed P 6.1.2.2 Determining the electrical charge of the electron after Millikan and demonstrating the quantum nature of the charge – measuring the rising speed and the falling speed Determining the electrical charge of the electron after Millikan and demonstrating the quantum nature of the charge – measuring the suspension voltage and the falling speed (P 6.1.2.1) With his famous oil-drop method, R. A. Millikan succeeded in demonstrating the quantum nature of minute amounts of electricity in 1910. He caused charged oil droplets to be suspended in the vertical electric field of a plate capacitor and, on the basis of the radius r and the electric field E, determined the charge q of a suspended droplet: 4S 3 U · g q= ·r · 3 E U: density of oil g: gravitational acceleration He discovered that q only occurs as a whole multiple of an electron charge e. His experiments are produced here in two variations. In the first variation, the electric field U E= d d: plate spacing is calculated from the voltage U at the plate capacitor at which the observed oil droplet just begins to hover. The constant falling velocity v1 of the droplet when the electric field is switched off is subsequently measured to determine the radius. From the equilibrium between the force of gravity and Stokes friction, we derive the equation 4S 3 · r · U · g = 6S · r · J · v1 3 J: viscosity In the second variant, the oil droplets are observed which are not precisely suspended, but which rise with a low velocity v2. The following applies for these droplets: U 4S 3 q· = r · U · g + 6S · r · J · v2 d 3 Cat. No. Description 559 411 559 421 Millikan apparatus Power supply for Millikan apparatus Electronic stopclock P Pair of cables, 1 m, red and blue P 6.1.2.1 1 1 1 3 1 2 313 033 501 46 The histogram reveals the quantum nature of the change Additionally, the falling speed v1 is measured, as in the first variant. The measuring accuracy for the charge q can be increased by causing the oil droplet under study to rise and fall over a given distance several times in succession and measuring the total rise and fall times. 206 P 6.1.2.2 1 4 Atomic and nuclear physics Introductory experiments P 6.1.3 Specific electron charge P 6.1.3.1 Determining the specific charge of the electron Determining the specific charge of the electron (P 6.1.3.1) Cat. No. 555 571 555 581 521 65 521 545 Description Fine beam tube Helmholtz coils with holder and measuring device DC power supply 0....500 V DC power supply 0....16 V, 5 A Voltmeter, DC, U ≤ 300 V, e. g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 3 A, e. g. Multimeter METRAmax 2 Teslameter Axial B-probe Multicore cable, 6-pole, 1.5 m long Steel tape measure, 2m Safety connection lead, 25 cm, black Safety connection lead, 50 cm, black Safety connection lead, 100 cm, black * additionally recommended 1 1 1 1 1 1 1* 1* 1* 1 3 3 7 The mass me of the electron is extremely difficult to determine in an experiment. It is much easier to determine the specific charge of the electron e Z= me from which we can calculate the mass me for a given electron charge e. In this experiment, a tightly bundled electron beam is diverted into a closed circular path using a homogeneous magnetic field in order to determine the specific electron charge. The magnetic field B which diverts the electrons into the path with the given radius r is determined as a function of the acceleration voltage U. The Lorentz force caused by the magnetic field acts as a centripetal force. It depends on the velocity of the electrons, which in turn is determined by the acceleration voltage. The specific electron charge can thus be determined from the measurement quantities U, B and r according to the formula e U =2 · 2 2. me B ·r 531 100 531 100 516 62 516 61 501 16 311 77 500 614 500 624 500 644 P 6.1.3.1 Circular electron path in fine beam tube 207 Introductory experiments P 6.1.4 Planck’s constant Atomic and nuclear physics P 6.1.4.1 Determining Planck’s constant – measuring with a compact assembly P 6.1.4.2 Determining Planck’s constant – dispersion of wavelengths with a direct-vison prism on the optical bench Determining Planck’s constant – measuring with a compact assembly (P 6.1.4.1) P 6.1.4.2 P 6.1.4.1 Cat. No. 558 77 558 79 558 791 451 15 451 19 Description Photo cell for determining Planck's constant Compact arrangement for determining Planck's constant Supply unit for photo cell High-pressure mercury lamp Lamp socket E27 on rod for high-pressure mercury lamp Cat. No. 451 30 532 14 Description Universal choke 230 V, 50 Hz Electrometer amplifier Plug-in unit 230V/12 V AC/20 W; with female plug I-measuring amplifier D Multimeter METRAmax 2 Screened cable BNC/4 mm Rastered socket panel, DIN A4 STE mono cell holder STE 10-turn potentiometer 1 kE, 2 W STE capacitor 100 pF, 630 V STE key switch (n.o.), single-pole Set of 10 bridging plugs Set of 20 batteries 1.5 V (type MONO) Precision optical bench, standardized cross section, 1 m Auxiliary bench w. swivel joint, protractor and index bench, 0.5 m Optics rider, H = 90 mm/W =50 mm Optics rider, H = 120 mm/W = 50 mm Lens f = + 50 mm Lens f = + 150 mm Adjustable slit Projection objective, f = + 150 mm Direct-vision prism Holder for direct-vision prism Distribution box Clamping plug Connection lead, black, 25 cm Connection lead, yellow-green, 100 cm Connection lead, black, 100 cm Pair of cables, 50 cm, red and blue Pair of cables, 1 m, black 1 1 1 1 1 1 1 1 1 1 562 791 532 00 531 100 575 24 1 1 When light with the frequency V falls on the cathode of a photocell, electrons are released. Some of the electrons reach the anode where they generate a current in the external circuit, which is compensated to zero by applying a voltage with opposite sign U = –U0 . The applicable relationship e · U0 = h · V – W, W: electronic work function was first used by R. A. Millikan to determine Planck’s constant h. In the first experiment, a compact arrangement is used to determine h, in which the light from a high-pressure mercury vapor lamp is spectrally dispersed in a direct-vision prism. The light of precisely one spectral line at a time falls on the cathode. A capacitor is connected between the cathode and the anode of the photocell which is charged by the anode current, thus generating the opposing voltage U. As soon as the opposing voltage reaches the value –U0, the anode current is zero and the charging of the capacitor is finished. U0 is measured without applying a current by means of an electrometer amplifier. The second experiment uses an open arrangement on the optical bench. Here as well, the wavelengths of the light are dispersed using a direct-vision prism. The opposing voltage U is tapped from a DC voltage source via a voltage divider, and varied until the anode current is compensated precisely to zero. The I-measuring amplifier D is used for conducting sensitive measurements of the anode current. 576 74 576 86 577 93 578 22 579 10 501 48 503 11 460 32 460 34 460 352 460 357 460 02 460 08 460 14 460 13 466 05 466 04 502 04 590 011 500 414 500 440 500 444 501 45 501 461 1 1 1 1 1 1 2 5 1 1 1 1 1 1 1 2 1 1 1 1 1 2 208 P 6.1.4.2 1 1 2 1 2 1 P 6.1.4.1 Atomic and nuclear physics Introductory experiments P 6.1.4 Planck’s constant P 6.1.4.3 Determining Planck’s constant – selection of wavelengths with interference filters on the optical bench Determining Planck’s constant – selection of wavelengths with interference filters on the optical bench (P 6.1.4.3 a) Cat. No. Description 558 77 558 791 451 15 451 19 460 03 460 26 558 792 468 401 468 402 468 403 468 404 451 30 532 14 562 791 578 22 579 10 531 100 460 34 460 32 460 352 460 357 590 011 501 10 501 09 340 89 500 440 501 45 502 04 Photo cell for determining Planck's constant Supply unit for photo cell High-pressure mercury lamp Lamp socket E27 on rod for high-pressure mercury lamp Lens f = + 100 mm Iris diaphragm Filter wheel with iris diaphragm Interference filter 578 nm Interference filter 546 nm Interference filter 436 nm Interference filter 405 nm Universal choke 230 V, 50 Hz Electrometer amplifier Plug-in unit 230V/12 V AC/20 W; with female plug STE capacitor 100 pF, 630 V STE key switch n.o. single-pole Multimeter METRAmax 2 Auxiliary bench with swivel joint Precision optical bench, standardized cross section, 1 m Optics rider, H = 90 mm/W =50 mm Optics rider, H = 120 mm/W = 50 mm Clamping plug Straight BNC BNC adapter for 4 mm socket, 1-pole Coupling plug Connection lead, 100 cm Pair of cables, 50 cm, red and blue Distribution box 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 In determining Planck's constant using the photoelectric effect, it must be ensured that only the light of a single spectral line of the high-pressure mercury vapor lamp falls on the cathode of the photocell at any one time. As an alternative to a prism, it is also possible to use narrow-band interference filters to select the wavelength. This simplifies the subsequent optical arrangement, and it is no longer necessary to darken the experiment room. Also, the intensity of the light incident on the cathode can be easily varied using an iris diaphragm. In this experiment, the capacitor method described previously (see P 6.1.4.1) is used to generate the opposing voltage U between the cathode and the anode of the photocell. The voltage at the capacitor is measured without current using the electrometer amplifier. Note: The opposing voltage U can alternatively be tapped from a DC voltage source. The I-measuring amplifier D is recommended for sensitive measurements of the anode current (see P 6.1.4.2). 2 3 2 1 1 1 2 1 1 P 6.1.4.3 (b) 1 2 3 2 1 1 1 2 1 1 P 6.1.4.3 (a) 209 Introductory experiments P 6.1.5 Dualism of wave and particle P 6.1.5.1 Diffraction of electrons in a polycrystalline lattice (Debye-Scherrer diffraction) P6.1.5.2 Optical analogy to diffraction of electrons in a polycrystalline lattice Atomic and nuclear physics Diffraction of electrons in a polycrystalline lattice (Debye-Scherrer diffraction) (P 6.1.5.1) In 1924, L. de Broglie first hypothesized that particles could have wave properties in addition to their familiar particle properties, and that their wavelength depends on the linear momentum p h Ö= h: Planck’s constant p His conjecture was confirmed in 1927 by the experiments of C. Davisson and L. Germer on the diffraction of electrons at crystalline structures. The first experiment demonstrates diffraction of electrons at polycrystalline graphite. As in the Debye-Scherrer method with xrays, we observe diffraction rings in the direction of radiation which surround a central spot on a screen. These are caused by the diffraction of electrons at the lattice planes of microcrystals which fulfill the Bragg condition 2 · d · sin P = n · Ö P: angular aperture of diffraction ring d: spacing of lattice planes As the graphite structure contains two lattice-plane spacings, two diffraction rings in the first order are observed. The electron wavelength h Ö= ö2 · me · e · U me: mass of electron, e: elementary charge is determined by the acceleration voltage U, so that for the angular aperture of the diffraction rings we can say 1 sin P “ . öU The second experiment illustrates the Debye-Scherrer method used in the electron diffraction tube by means of visible light. Here, parallel, monochromatic light passes through a rotating crossed grating. The diffraction pattern of the crossed grating at rest, consisting of spots of light arranged around the central beam in a network-like pattern, is deformed by rotation into rings arranged concentrically around the central spot. 210 Cat. No. 555 626 555 600 Description Electron diffraction tube Stand rod for electron tubes High voltage power supply 10 kV Safety connection lead, 25 cm, red Safety connection lead, 50 cm, red Safety connection lead, 100 cm, red Cross grating, rotatable 1 1 1 1 1 1 521 70 500 611 500 621 500 641 555 629 450 63 450 64 450 66 521 25 460 03 Halogen lamp, 12 V/100 W Halogen lamp housing, 12 V, 50/100W Picture slider for halogen lamp housing Transformer 2....12 V Lens f = + 100 mm 441 53 460 43 301 01 300 01 501 46 500 642 500 644 Translucent screen Small optical bench Leybold multiclamp Stand base, V-shape, 28 cm I Safety connection lead, 100 cm, blue I Safety connection lead, 100 cm, black Pair of cables, 1 m, red and blue I1I I2I Optical analogon of Debye-Scherrer diffraction (P 6.1.5.2) P 6.1.5.2 1 1 1 1 1 1 1 1 P 6.1.5.1 5 1 1 Atomic and nuclear physics Introductory experiments P 6.1.6 Paul trap P 6.1.6.1 Observing individual lycopod spores in a Paul trap Observing individual lycopod spores in a Paul trap (P 6.1.6.1) Cat. No. Description 558 80 471 830 Paul trap He-Ne laser, linearly polarized Lens f = + 5 mm Auxiliary bench w. swivel joint, 0.5 m Precision optical bench, standardized cross section, 1 m Optics rider, H = 60 mm/W = 50 mm Power supply 450 V DC Variable extra low voltage transformer S U-core with yoke Clamping device Extra-low voltage coil, 50 turns Coil with 10,000 turns Multimeter METRAmax 2 Measuring resistor 10 ME, 1 W Safety connection lead, 100 cm, black Safety connection lead, 50 cm, black Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue Set of 6 safety adapter sockets, black Pair of cables, 50 cm, red and blue Connection lead, 100 cm, yellow/green Distribution box 1 1 1 1 1 1 1 460 01 460 34 460 32 460 351 522 27 521 35 562 11 562 12 562 18 562 16 531 100 536 211 500 644 500 624 500 641 500 642 500 98 501 45 500 440 502 04 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 Spectroscopic measurements of atomic energy levels are normally impaired by the motion of the atoms under study with respect to the radiation source. This motion shifts and broadens the spectral lines due to the Doppler effect, which becomes strongly apparent in high-resolution spectroscopy. The influence of the Doppler effect is reduced when individual atoms are enclosed in a small volume for spectroscopic measurements. For charged particles (ions), this can be achieved using the ion trap developed by W. Paul in the 1950's. This consists of two rotationally symmetrical cover electrodes and one ring electrode. The application of an AC voltage generates a time-dependent, parabolic potential with the form r 2 – 2z 2 U(r, z, t) = U0 · cos Ct · 2 · r2 0 z: coordinate on the axis of symmetry, r: coordinate perpendicular to axis of symmetry, r0: inside radius of ring electrode An ion with the charge q and the mass m remains trapped in this potential when the conditions q r 2 · C2 0.4 · R < < 1.2 R where R = 0 m U0 are fulfilled. This experiment demonstrates how a Paul trap works using a model which can be operated with no special requirements at standard air pressure and with 50 Hz AC. When a suitable voltage amplitude U0 is set, it is possible to trap lycopod spores for several hours and observe them under laser light. Tilting of the entire ion trap causes the trapped particles to move radially within the ring electrode. When a voltage is applied between the cover electrodes, it is possible to shift the potential along the z-axis. P 6.1.6.1 (b) P 6.1.6.1 (a) 211 Atomic shells P 6.2.1 The Balmer series of hydrogen P 6.2.1.1 Determining the wavelengths HR, HT and HH from the Balmer series of hydrogen P 6.2.1.2 Observing the Balmer series of hydrogen using a prism spectrometer Atomic and nuclear physics Determining the wavelengths HR, HT and HH from the Balmer series of hydrogen (P 6.2.1.1) In the visible range, the emission spectrum of atomic hydrogen has four lines, HR, HT, HH and HF; this sequence continues into the ultraviolet range to form a complete series. In 1885, Balmer empirically worked out a formula for the frequencies of this series 1 1 V = R∞, · , m: 3, 4, 5, ... – 2 m2 2 Cat. No. 451 13 451 14 471 23 311 77 460 02 460 03 460 14 460 22 441 53 460 43 300 01 301 01 467 112 Description Balmer lamp Power supply unit for Balmer lamps Copy of a Rowland grating, approx. 5700 lines/cm Steel tape measure, 2 m Lens f = + 50 mm Lens f = + 100 mm Adjustable slit Holder with spring clips Translucent screen Small optical bench Stand base, V-shape, 28 cm Leybold multiclamp School spectroscope 1 1 1 1 1 1 1 1 1 1 1 6 ( ) R∞ = 3.2899 · 1015 s–1: Rydberg constant which could later be explained using Bohr’s model of the atom. In this experiment, the emission spectrum is excited using a Balmer lamp filled with water vapor, in which an electric discharge splits the water molecules into an excited hydrogen atom and a hydroxyl group. The wavelengths of the lines HR, HT and HH are determined using a high-resolution grating. In the first diffraction order of the grating, we can find the following relationship between the wavelength Ö and the angle of observation P: Ö = d · sin P d: grating constant The measured values are compared with the values calculated according to the Balmer formula. In the second experiment the Balmer series are studied by means of a prism spectroscope (complete device). Emission spectrum of atomic hydrogen Observing the Balmer series of hydrogen using a prism spectrometer (P 6.2.1.2) 212 P 6.2.1.2 1 1 1 P 6.2.1.1 Atomic and nuclear physics Atomic shells P 6.2.2 Emission and absorption spectra P 6.2.2.1 Displaying the line spectra of inert gases and metal vapors P 6.2.2.2 Qualitative investigation of the absorption spectrum of sodium Displaying the line spectra of inert gases and metal vapors (P 6.2.2.1) Cat. No. 451 011 451 041 451 062 451 111 451 16 451 30 460 02 460 03 471 23 460 14 460 22 441 53 311 77 460 43 300 01 301 01 673 5700 Description Spectral lamp Ne Spectral lamp Cd Spectral lamp Hg 100 Spectral lamp Na Housing for spectral lamps with pin contact Universal choke 230 V, 50 Hz Lens f = + 50 mm Lens f = + 100 mm Copy of a Rowland grating, approx. 5700 lines/cm Adjustable slit Holder with spring clips Translucent screen Steel tape measure, 2 m Small optical bench Stand base, V-shape, 28 cm Leybold multiclamp Sodium chloride, 250 g Spatula, double-ended, 150 mm, 9 mm wide, stainless steel Butane gas burner, gas and air regulation valve Butane gas cartridges, 200 g, set of 3, for 666 711/713 Lamp housing Lamp, 6 V/30 W Transformer, 6 V AC, 12 V AC/30 VA 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 2 1 1 1 1 1 1 1 When an electron in the shell of an atom or atomic ion drops from an excited state with the energy E2 to a state of lower energy E1, it can emit a photon with the frequency E – E1 O= 2 h h: Planck’s constant In the opposite case, a photon with the same frequency is absorbed. As the energies E1 and E2 can only assume discrete values, the photons are only emitted and absorbed at discrete frequencies. The totality of the frequencies which occur is referred to as the spectrum of the atom. The positions of the spectral lines are characteristic of the corresponding element. The first experiment disperses the emission spectra of metal vapors and inert gases (mercury, sodium, cadmium and neon) using a high-resolution grating and projects these on the screen for comparison purposes. In the second experiment, the flame of a Bunsen burner is alternately illuminated with white light and sodium light and observed on a screen. When sodium is burned in the flame, a dark shadow appears on the screen when illuminating with sodium light. From this it is possible to conclude that the light emitted by a sodium lamp is absorbed by the sodium vapor, and that the same atomic components are involved in both absorption and emission. 666 962 666 711 666 712 450 60 450 51 521 210 300 02 300 11 300 42 Stand base, V-shape, 20 cm Saddle base Stand rod, 47 cm P 6.2.2.2 1 1 1 1 2 1 2 P 6.2.2.1 213 Atomic shells P 6.2.3 Inelastic electron collisions Atomic and nuclear physics P 6.2.3.1 Discontinuous energy emission of electrons in a gas-filled triode Discontinuous energy emission of electrons in a gas-filled triode (P 6.2.3.1) In inelastic collision of an electron with an atom, the kinetic energy of the electron is transformed into excitation or ionization energy of the atom. Such collisions are most probable when the kinetic energy is exactly equivalent to the excitation or ionization energy. As the excitation levels of the atoms can only assume discrete values, the energy emission in the event of inelastic electron collision is discontinuous. This experiment uses tube triodes filled with helium or neon to demonstrate this discontinuous emission of energy. After acceleration in the electric field between the cathode and the grid, the electrons enter an opposing field which exists between the grid and the anode. Only those electrons with sufficient kinetic energy reach the anode and contribute to the current I flowing between the anode and ground. Once the electrons in front of the grid have reached a certain minimum energy (which depends on the gas), they can excite the gas atoms through inelastic collision. When the acceleration voltage U is continuously increased, the inelastic collisions initially occur directly in front of the grid, as the kinetic energy of the electrons reaches its maximum value here. After collision, the electrons can no longer travel against the opposing field. The anode current I is thus greatly decreased. When the acceleration voltage U is increased further, the excitation zone moves toward the cathode, the electrons can again accumulate energy on their way to the grid and the current I again increases. Finally, the electrons can excite gas atoms a second time, and the anode current drops once more. Cat. No. 555 614 555 600 Description Gas filled triode Stand for electron tubes DC power supply 0....500 V Voltmeter, DC, U < 100 V, e. g. Multimeter METRAmax 2 Amperemeter, DC, I < 100 µA, e. g. Multimeter METRAmax 2 1 1 1 2 521 65 531 100 531 100 1 500 621 Safety connection lead, 50 cm, red 1 4 6 500 641 500 642 Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue Anode current I as a function of the acceleration voltage U for He 214 P 6.2.3.1 Atomic and nuclear physics Atomic shells P 6.2.4 Franck-Hertz experiment P 6.2.4.1 Franck-Hertz experiment with mercury – recording with the oscilloscope, the XY recorder or point by point P 6.2.4.2 Franck-Hertz experiment with mercury – measuring and evaluating with CASSY Franck-Hertz experiment with mercury – recording with the oscilloscope (P 6.2.4.1 b) Cat. No. Description 555 85 555 861 555 81 555 88 666 193 575 211 575 24 575 664 Mercury Franck-Hertz tube Socket for Franck-Hertz-tube with multi-pin plug Electric oven, 230 V Franck-Hertz supply unit Temperature sensor NiCr-Ni Two-channel oscilloscope 303 Screened cable BNC/4 mm XY-Yt recorder Pair of cables, 1 m, red and blue Sensor CASSY CASSY Lab additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 501 46 524 010 524 200 In 1914, J. Franck and G. Hertz reported observing discontinuous energy emission when electrons passed through mercury vapor, and the resulting emission of the ultraviolet spectral line (Ö = 254 nm) of mercury. A few months later, Niels Bohr recognized that their experiment supported his model of the atom. This experiment is offered in two variations, which differ only in the means of recording and evaluating the measurement data. The mercury atoms are enclosed in a tetrode with cathode, gridtype control electrode, acceleration grid and target electrode. The control grid ensures a virtually constant emission current of the cathode. An opposing voltage is applied between the acceleration grid and the target electrode. When the acceleration voltage U between the cathode and the acceleration grid is increased, the target current I corresponds closely to the tube characteristic once it rises above the opposing voltage. As soon as the electrons acquire sufficient kinetic energy to excite the mercury atoms through inelastic collisions, the electrons can no longer reach the target, and the target current drops. At this acceleration voltage, the excitation zone is directly in front of the excitation grid. When the acceleration voltage is increased further, the excitation zone moves toward the cathode, the electrons can again accumulate energy on their way to the grid and the target current again increases. Finally, the electrons can excite the mercury atoms once more, the target current drops again, and so forth. The I(U) characteristic thus demonstrates periodic variations, whereby the distance between the minima WU = 4.9 V corresponds to the excitation energy of the mercury atoms from the ground state 1S0 to the first 3P1 state. P 6.2.4.1(b) P 6.2.4.1(a) P 6.2.4.1(c) Franck-Hertz curve P 6.2.4.2 215 Atomic shells P 6.2.4 Franck-Hertz experiment Atomic and nuclear physics P 6.2.4.3 Franck-Hertz experiment with neon – recording with the oscilloscope, the XY recorder or point by point P 6.2.4.4 Franck-Hertz experiment with neon – measuring and evaluating with CASSY Franck-Hertz experiment with neon (P 6.2.4.4) When neon atoms are excited by means of inelastic electron collision at a gas pressure of approx. 10 hPa, excitation is most likely to occur to states which are 18.7 eV above the ground state. The de-excitation of these states can occur indirectly via intermediate states, with the emission of photons. In this process, the photons have a wavelength in the visible range between red and green. The emitted light can thus be observed with the naked eye and e. g. measured using the school spectroscope Kirchhoff/Bunsen (467 112). The Franck-Hertz experiment with neon is offered in two variations, which differ only in the means of recording and evaluating the measurement data. In both variations, the neon atoms are enclosed in a glass tube with four electrodes: the cathode K, the grid-type control electrode G1, the acceleration grid G2 and the target electrode A. Like the Franck-Hertz experiment with mercury, the acceleration voltage U is continuously increased and the current I of the electrons which are able to overcome the opposing voltage between G2 and A and reach the target is measured. The target current is always lowest when the kinetic energy directly in front of grid G2 is just sufficient for collision excitation of the neon atoms, and increases again with the acceleration voltage. We can observe clearly separated luminous red layers between grids G1 and G2; their number increases with the voltage. These are zones of high excitation density, in which the excited atoms emit light in the visible spectrum. P 6.2.4.3(b) P 6.2.4.3(a) P 6.2.4.3(c) 1 1 1 1 1 2 Cat. No. Description 555 870 555 871 555 872 555 88 575 211 575 24 575 664 Neon Franck-Hertz tube Holder with socket and screen for neon FH tube 1 1 1 1 1 1 1 1 1 2 1 1 1 1 Connecting cable for Ne-FH Franck-Hertz supply unit Two-channel oscilloscope 303 Screened cable BNC/4 mm XY-Yt recorder Sensor CASSY CASSY Lab Pair of cables, 1 m, red and blue additionally required: PC with Windows 95/NT or higher 524 010 524 200 50146 1 1 2 1 Luminous layers between control electrode and acceleration grid 216 P 6.2.4.4 Atomic shells P 6.2.6 Electron spin resonance (ESR) Atomic and nuclear physics P 6.2.6.2 Electron spin resonance in DPPH – determining the magnetic field as a function of the resonance frequency P 6.2.6.3 Resonance absorption of a passive RF oscillator circuit Electron spin resonance in DPPH – determining the magnetic field as a function of the resonance frequency (P 6.2.6.2) The magnetic moment of the unpaired electron with the total angular momentum j in a magnetic field assumes the discrete energy states Em = – gj · BB · m · B where m = –j, –j + 1, ... , j J BB = 9,274 · 10–24 : Bohr’s magneton T gj: g factor When a high-frequency magnetic field with the frequency V is applied perpendicularly to the first magnetic field, it excites transitions between the adjacent energy states when these fulfill the resonance condition h · V = Em+1 – Em h: Planck’s constant. This fact is the basis for electron spin resonance, in which the resonance signal is detected using radio-frequency technology. The electrons can often be regarded as free electrons. The g-factor then deviates only slightly from that of the free electron (g = 2.0023), and the resonance frequency V in a magnetic field of 1 mT is about 78.0 MHz. The actual aim of electron spin resonance is to investigate the internal magnetic fields of the sample substance, which are generated by the magnetic moments of the adjacent electrons and nuclei. The first two experiments verify electron spin resonance in diphenyl-picryl-hydrazyl (DPPH). DPPH is a radical, in which a free electron is present in a nitrogen atom. In the simple configuration of the first experiment, the magnetic field B which fulfills the resonance condition is determined for three different resonance frequencies V. In the second experiment, the resonance frequencies can be set in a continuous range from 13 to 130 MHz. The aim of the evaluation in both cases is to determine the g factor. The object of the final experiment is to verify resonance absorption using a passive oscillator circuit. 218 P 6.2.6.2 1 1 1 1 2 Cat. No. Description 514 55 514 57 555 604 ESR basic unit ESR control unit Pair of Helmholtz coils 575 211 575 24 531 100 531 100 531 100 300 11 590 13 501 28 501 23 Two-channel oscilloscope 303 Screened cable BNC/4 mm Ammeter, DC, I ≤ 3 A, e.g. Multimeter METRAmax 2 Voltmeter, AC, U ≤ 1 V, e.g. Multimeter METRAmax 2 Ammeter, DC, I ≤ 1 mA, e.g. Multimeter METRAmax 2 Stand base Insulated stand rod, 25 cm Connecting lead, Ø 2.5 mm2, 50 cm, black Connecting lead, Ø 2.5 mm2, 25 cm, black 1 1 1 3 3 2 Diagram of resonance condition of free electrons P 6.2.6.3 1 1 2 1 2 Atomic and nuclear physics Atomic shells P 6.2.7 Normal Zeeman effect P 6.2.7.1 Observing the normal Zeeman effect in transverse and longitudinal configuration – spectroscopy using a LummerGehrcke plate P 6.2.7.2 Measuring the Zeeman split of the red cadmium line as a function of the magnetic field – spectroscopy using a LummerGehrcke plate P 6.2.7.3 Observing the normal Zeeman effect in transverse and longitudinal configuration – spectroscopy using a FabryPerot etalon P 6.2.7.4 Measuring the Zeeman split of the red cadmium line as a function of the magnetic field – spectroscopy using a FabryPerot etalon Measuring the Zeeman split of the red cadmium line as a function of the magnetic field (P 6.2.7.4) Cat. No. Description 451 12 451 30 521 55 514 50 471 20 471 21 562 11 562 131 560 315 471 221 460 32 460 358 460 351 460 08 472 601 472 401 460 22 467 95 468 41 468 400 460 135 337 47 516 62 516 60 501 16 300 02 300 42 301 01 501 33 501 20 501 21 501 30 501 31 Cadmium lamp for Zeeman-Effekt Universal choke, in housing, 230 V, 50 Hz High current power supply Electromagnet for Zeeman-Effect Optical system for observing the Zeeman-Effect Lummer-Gehrcke plate U-core with yoke Coil, 10 A, 480 turns Pair of pole pieces with great bore Fabry-Perot etalon Precision optical bench, stand. cross section, 1 m Rider base, Width: 148 mm Optics rider, H = 60 mm/W = 50 mm Lens, f = + 150 mm Quarter-wavelength plate Polarization filter Holder with spring clips Filter set red, green, blue Holder for interference filters Interference filter, 644 nm Ocular with scale VideoCom Teslameter Tangential B-probe Multicore cable, 6-pole, 1.5 m long Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Connecting lead, Ø 2.5 mm2, 100 cm, black Connecting lead, Ø 2.5 mm2, 25 cm, red Connecting lead, Ø 2.5 mm2, 25 cm, blue Connecting lead, Ø 2.5 mm2, 100 cm, red Connecting lead, Ø 2.5 mm2, 100 cm, blue add. required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 7 2 1 1 1 1 1 2 1 1 1 1 7 2 1 1 1 2 1 1 1 1 5 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 The Zeeman effect is the name for the splitting of atomic energy levels in an external magnetic field and, as a consequence, the splitting of the transitions between the levels. The effect was predicted by H. A. Lorentz in 1895 and experimentally confirmed by P. Zeeman one year later. In the red spectral line of cadmium (Ö = 643.8 nm), Zeeman observed a line triplet perpendicular to the magnetic field and a line doublet parallel to the magnetic field, instead of just a single line. Later, even more complicated splits were discovered for other elements, and were collectively designated the anomalous Zeeman effect. It eventually became apparent that the normal Zeeman effect is the exception, as it only occurs at transitions between atomic levels with the total spin S = 0. In the first and third experiment, the Zeeman effect is observed at the red cadmium line perpendicular and parallel to the magnetic field, and the polarization state of the individual Zeeman components is determined. The observations are explained on the basis of the radiating characteristic of dipole radiation. The so-called S component corresponds to a Hertzian dipole oscillating parallel to the magnetic field, i. e. it cannot be observed parallel to the magnetic field and radiates linearly polarized light perpendicular to the magnetic field. Each of the two D components corresponds to two dipoles oscillating perpendicular to each other with a phase differential of 90°. They radiate circularly polarized light in the direction of the magnetic field and linearly polarized light parallel to it. In the second and fourth experiment, the Zeeman splitting of the red cadmium line is measured as a function of the magnetic field B. The energy interval of the triplet components h e WE = · ·B 4S me me: mass of electron, e: electron charge, h: Planck’s constant B: magnetic induction P 6.2.7.3(b) P 6.2.7.3(a) P 6.2.7.2 P 6.2.7.4 1 P 6.2.7.1 is used to calculate the specific electron charge. 219 Atomic shells P 6.2.8 Optical pumping (anomalous Zeeman effect) P 6.2.8.1 Optical pumping: observing the pumping signal P 6.2.8.2 Optical pumping: measuring and observing the Zeeman transitions in the ground state of Rb-87 with D+ and D- pumped light P 6.2.8.3 Optical pumping: measuring and observing the Zeeman transitions in the ground state of Rb-85 with D+ and D- pumped light P 6.2.8.4 Optical pumping: measuring and observing the Zeeman transitions in the ground state of Rb-87 as a function of the magnetic flux density B P 6.2.8.5 Optical pumping: measuring and observing the Zeeman transitions in the ground state of Rb-85 as a function of the magnetic flux density B P 6.2.8.6 Optical pumping: measuring and observing twoquantum transitions Atomic and nuclear physics Measuring and observing the Zeeman transitions in the ground state of Rb-87 with D+- pumped light (P 6.2.8.2) The two hyperfine structures of the ground state of an alkali atom with the total angular momentums 1 1 F+ = l + , F– = l – 2 2 split in a magnetic field B into 2F± + 1 Zeeman levels having an energy which can be described using the Breit-Rabi formula –∆ E ∆E 4mF E= + BK gl mF ± 1+ K + K2 2 (2 l + 1) 2 2l + 1 g B – gl BK where K = J B ·B ∆E ∆E: hyperfine structure interval, I: nuclear spin, mF: magnetic quantum number, BB: Bohr’s magneton, BK: nucelar magneton, gJ: shell g factor, gI: nuclear g factor Transitions between the Zeeman levels can be observed using a method developed by A. Kastler. When right-handed or left-handed circularly polarized light is directed parallel to the magnetic field, the population of the Zeeman level differs from the thermal equilibrium population, i. e. optical pumping occurs, and RF radiation forces transitions between the Zeeman levels. The change in the equilibrium population when switching from right-handed to left-handed circular pumped light is verified in the first experiment. The second and third experiments measure the Zeeman transitions in the ground state of the isotopes Rb-87 and Rb-85 and determine the nuclear spin I from the number of transitions observed. The observed transitions are classified through comparison with the Breit-Rabi formula. In the next two experiments, the measured transition frequencies are used for precise determination of the magnetic field B as a function of the magnet current I. The nuclear g factors gI are derived using the measurement data. In the final experiment, two-quantum transitions are induced and observed for a high field strength of the irradiating RF field. Cat. No. Description 558 820 558 825 558 830 558 835 558 836 530 88 558 811 521 45 522 551 501 022 501 02 575 294 531 582 504 48 468 000 472 410 472 611 460 021 460 031 460 32 460 353 460 352 666 768 Rubidium high frequency lamp Helmholtz coils on stand rider Absorption chamber with rubidium absorption cell Silicon photodetector I/U-converter for silicon photodetector Plug-in power unit, 9.2 V DC, regulated Operational device for optical pumping DC power supply 0....+/- 15 V Function generator, 12 MHz, internal sweep BNC cable, 2 m long BNC cable, 1 m long Two channel/ XY storage oscilloscope, e.g. Analog/digital oscilloscope HM 507 Multimeter METRAport 32 S Two-way switch Line filter 795 nm Polarization filter Quarter-wavelength plate (200 nm) Lens f = + 50 mm, brass handle Lens f = + 100 mm, brass handle Precision optical bench, standardized cross section, 1 m Optics rider, H = 60 mm/W = 36 mm Optics rider, H = 90 mm/W =50 mm Circulation thermostat 30 ... 100 °C Connecting lead, Ø 2.5 mm2, 50 cm, black Connecting lead, Ø 2.5 mm2, 100 cm, black 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ö 2 1 1 1 1 1 1 2 1 1 7 1 1 4 3 1 1 1 1 1 1 2 1 1 7 1 1 4 200 66843 Silicone tube, 1.0 m long, 6.0 x 2.0 501 28 501 38 4 2 4 2 220 P 6.2.8.2-6 P 6.2.8.1 Atomic and nuclear physics P 6.3.1 Detection of x-rays X-rays P 6.3.1.1 Fluorescence of a luminescent screen due to x-rays P 6.3.1.2 X-ray photography: exposure of film stock due to x-rays P 6.3.1.3 Detecting x-rays using an ionization chamber P 6.3.1.4 Determining the ion dose rate of the x-ray tube with molydenum anode Determining the ion dose rate of the x-ray tube with molydenum anode (P 6.3.1.4) Cat. No. 554 811 554 838 Description X-ray apparatus X-ray film holder 1 1 1 1 554 896 554 840 522 27 532 14 577 02 531 100 531 100 575 24 501 451 501 46 501 45 X-ray film Agfa Dentus M2 Plate capacitor x-ray Power supply 450 V DC Electrometer amplifier STE resistor 1 GV, 0.5 W Voltmeter, DC, U ≤ 300 V, e. g. Multimeter METRAmax 2 Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax 2 Screened cable BNC/4 mm Pair of cables, 50 cm, black Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 1 1 1 554 897 554 898 I Developer for X-ray film I Fixative for X-ray film Pair of cables, 50 cm, red and blue I I1I I I1I 2 Soon after the discovery of x-rays by W. C. Röntgen, physicians began to exploit the ability of this radiation to pass through matter which is opaque to ordinary light for medical purposes. The technique of causing a luminescent screen to fluoresce with xray radiation is still used today for screen examinations, although image amplifiers are used additionally. The exposure of a film due to x-ray radiation is used both for medical diagnosis and materials testing, and is the basis for dosimetry with films. As x-rays ionize gases, they can also be measured via the ionization current of an ionization chamber. The first experiment demonstrates the transillumination with xrays using simple objects made of materials with different absorption characteristics. A luminescent screen of zinc-cadmium sulfate is used to detect x-rays; the atoms in this compound are excited by the absorption of x-rays and emit light quanta in the visible light range. This experiment investigates the effect of the emission current I of the x-ray tube on the brightness and the effect of the high voltage U on the contrast of the luminescent screen. The second experiment records the transillumination of objects using x-ray film. Measuring the exposure time required to produce a certain degree of exposure permits quantitative conclusions regarding the intensity of the x-rays. The aim of the last two experiments is to detect x-rays using an ionization chamber. First, the ionization current is recorded as a function of the voltage at the capacitor plates of the chamber and the saturation range of the characteristic curves is identified. Next, the mean ion dose rate I J = ion m is calculated from the ionization current Iion which the x-radiation generates in the irradiated volume of air V, and the mass m of the irradiated air. The measurements are conducted for various emission currents I and high voltages U of the x-ray tube. Fluorescence of a luminescent screen due to x-rays (P 6.3.1.1) P 6.3.1.3-4 P 6.3.1.2 P 6.3.1.1 221 X-rays P 6.3.2 Attenuation of x-rays Atomic and nuclear physics P 6.3.2.1 Investigating the attenuation of x-rays as a function of the absorber material and absorber thickness P 6.3.2.2 Investigating the wavelength dependency of the attenuation coefficient P 6.3.2.3 Investigating the relationship between the attenuation coefficient and the atomic number Z Investigating the attenuation of x-rays as a function of the absorber material and absorber thickness (P 6.3.2.1) The attenuation of x-rays on passing through an absorber with the thickness d is described by Lambert's law for attenuation: I = I0 · e–Bd I0: intensity of primary beam I: transmitted intensity Here, the attenuation is due to both absorption and scattering of the x-rays in the absorber. The linear attenuation coefficient B depends on the material of the absorber and the wavelength Ö of the x-rays. An absorption edge, i.e. an abrupt transition from an area of low absorption to one of high absorption, may be observed when the energy h · V of the x-ray quantum just exceeds the energy required to move an electron out of one of the inner electron shells of the absorber atoms. The object of the first experiment is to confirm Lambert's law using aluminum and to determine the attenuation coefficients B for six different absorber materials averaged over the entire spectrum of the x-ray apparatus. The second experiment records the transmission curves l (Ö) T(Ö) = l0(Ö) for various absorber materials. The aim of the evaluation is to confirm the Ö3 relationship of the attenuation coefficients for wavelengths outside of the absorption edges. In the final experiment, the attenuation coefficient B(Ö) of different absorber materials is determined for a wavelength Ö which lies outside of the absorption edge. This experiment reveals that the attenuation coefficient is closely proportional to the fourth power of the atomic number Z of the absorbers. P 6.3.2.2 1 1 1 1 Cat. No. 554 811 559 01 554 834 554 832 Description X-ray apparatus End-window counter for R, T, H- and x-rays Absorption accessory x-ray Set of absorber foils additionally required: 1 PC with Windows 95/NT or higher 1 1 1 1 1 1 222 P 6.3.2.3 P 6.3.2.1 Atomic and nuclear physics X-rays P 6.3.3 Physics of the atomic shell P 6.3.3.1 Bragg reflection: diffraction of x-rays at a monocrystal P 6.3.3.2 Investigating the energy spectrum of an x-ray tube as a function of the high voltage and the emission current P 6.3.3.3 Duane-Hunt relation and determination of Planck's constant P 6.3.3.4 Fine structure of the characteristic x-ray radiation of a molydenum anode P 6.3.3.5 Edge absorption: filtering x-rays P 6.3.3.6 Moseley's law and determination of the Rydberg constant P 6.3.3.7 Compton effect: verifying the energy loss of the scattered x-ray quantum P 6.3.3.8 Fine structure of the characteristic x-ray radiation of a copper anode Bragg reflection: diffraction of x-rays at a monocrystal (P 6.3.3.1) Cat. No. Description 554 811 554 85 559 01 554 832 554 836 X-ray apparatus Copper anode End-window counter for R-, T-, H- and x-rays Set of absorber foils Compton accessory x-ray additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The fourth experiment reveals the fine structure of the characteristic lines KR and KT and explains these on the basis of the fine structure of the atomic levels involved. The object of the fifth experiment is to filter x-rays using the absorption edge of an absorber, i. e. the abrupt transition from an area of low absorption to one of high absorption. The sixth experiment determines the wavelengths ÖK of the absorption edges as as function of the atomic number Z. When we apply Moseley's law 1 = R · (Z – D)2 ÖK to the measurement data we obtain the Rydberg constant R and the mean screening D. The final experiment verifies the Compton shift of the wavelength Ö in backscattering. This is apparent as a change in the attenuation coefficient of an absorber, which is placed in front of and then behind the scattering body. P 6.3.3.1-5 P 6.3.3.6 P 6.3.3.7 The radiation of an x-ray tube consists of two components: continuous bremsstrahlung radiation is generated when fast electrons are decelerated in the anode. Characteristic radiation consisting of discrete lines is formed by electrons dropping to the inner shells of the atoms of the anode material from which electrons were liberated by collision. To confirm the wave nature of x-rays, the first experiment investigates the diffraction of the chracteristic KR and KT lines of the molybdenum anode at an NaCl monocrystal and explains these using Bragg's law of reflection. The second experiment records the energy spectrum of the x-ray apparatus as a function of the high voltage and the emission current using a goniometer in the Bragg configuration. The aim is to investigate the spectral distribution of the continuum of bremsstrahlung radiation and the intensity of the characteristic lines. The third experiment measures how the limit wavelength Ömin of the continuum of bremsstrahlung radiation depends on the high voltage U of the x-ray tube. When we apply the Duane-Hunt relationship c e·U= h· e: electron charge, Ömin c: velocity of light to the measurement data, we can derive Planck's constant h. P 6.3.3.8 Splitting of the KR and KT-lines in the 3rd to 5th diffraction orders 223 Atomic and nuclear physics Radioactivity P 6.4.1 Detection of radioactivity P 6.4.1.1 Ionization of air due to radioactivity P 6.4.1.2 Recording the current-voltage characteristic of an ionization chamber P 6.4.1.3 Detecting radioactivity using a Geiger counter P 6.4.1.4 Recording the characteristic of a Geiger-Müller counter tube Ionization of air due to radioactivity (P 6.4.1.1) Cat. No. 559 82 546 31 546 33 522 27 532 14 532 16 577 03 531 100 546 25 521 70 532 00 575 24 501 644 300 02 300 41 301 01 666 555 559 430 546 281 546 38 575 211 300 11 559 01 575 48 590 13 591 21 500 412 500 421 Description Am 241 preparation Zinc plate for photoelectric effect Grid electrode Power supply 450 V DC Electrometer amplifier Connection rod STE resistor 10 GE, 0.5 W Voltmeter, DC, U ≤ 10 V, e. g. Multimeter METRAmax 2 Ionization chamber High voltage power supply 10 kV I-measuring amplifier D Screened cable BNC/4 mm Set of 6 two-way plug adapters, black Stand base, V-shape, 20 cm Stand rod, 25 cm Leybold multiclamp Universal clamp, 0...80 mm dia. Ra 226 preparation Geiger counter Adapter for geiger counter Two channel oscilloscope 303 Saddle base End-window counter for R, T, H and x-rays Digital counter Insulated stand rod, 25 cm long Large clip plug Connection lead, 25 cm, blue Connection lead, 50 cm, red 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 In 1895, H. Becquerel discovered radioactivity while investigating uranium salts. He found that these emitted a radiation which was capable of fogging light-sensitive photographic plates even through black paper. He also discovered that this radiation ionizes air and that it can be identified by this ionizing effect. In the first experiment, a voltage is applied between two electrodes, and the air between the two electrodes is ionized by radioactivity. The ions created in this way cause a charge transport which can be detected using an electrometer as a highly sensitive ammeter. The aim of the second experiment is to record the current-voltage characteristic of air ionized by radioactivity in an ionization chamber. This experiment shows that, at low voltages, the current rises in proportion to the voltage. At higher voltages, the current reaches a saturation value, which depends on the intensity of the preparation. The third experiment uses a Geiger counter to detect radioactivity. A potential is applied between a cover with hole which serves as the cathode and a fine needle as the anode; this potential is just below the threshold of the disruptive field strength of the air. As a result, each ionizing particle which travels within this field initiates a discharge collision. The final experiment records the current-voltage characteristic of a Geiger-Müller counter tube. Here too, the current increases proportionally to the voltage for low voltage values, before reaching a saturation value which depends on the intensity or distance of the preparation. P 6.4.1.2 P 6.4.1.3 P 6.4.1.4 P 6.4.1.1 500 610 501 40 501 45 Safety connecting lead, 25 cm, yellow/green Connecting lead, Ø 2.5 mm 2, 25 cm, yellow/green Pair of cables, 50 cm, red and blue Pair of cables, 50 cm, black 2 1 1 1 1 1 1 1 1 501 451 225 Radioactivity P 6.4.2 Poisson distribution Atomic and nuclear physics P 6.4.2.1 Statistical variations in determinating counting rates Statistical variations in determinating counting rates (P 6.4.2.1) For each individual particle in a radioactive preparation, it is a matter of coincidence whether it will decay over a given time period Wt. The probability that any particular particle will decay in this time period is extremely low. The number of particles n which will decay over time Wt thus shows a Poisson distribution around the mean value B. In other words, the probability that n decays will occur over a given time period Wt is Bn –B wB(n) = e n! B is proportional to the size of the preparation and the time Wt, and inversely proportional to the half-life T1/2 of the radioactive decay. Using a computer-assisted measuring system, this experiment determines multiple pulse counts n triggered in a Geiger-Müller counter tube by radioactive radiation over a selectable gate time Wt. After a total of N counting runs, the frequencies h(n) are determined at which precisely n pulses were counted, and displayed as histograms. For comparision, the evaluation program calculates the mean value B and the standard deviation D = öä B of the measured intensity distribution h(n) as well as the Poisson distribution wB(N). Cat. No. 559 83 559 01 524 033 524 010 524 200 591 21 590 02 532 16 300 11 Description Set of 5 radioactive preparations End-window counter for R, T, H and x-rays GM-box Sensor-CASSY CASSY Lab Large clip plug Small clip plug Connection rod Saddle base additionally required: PC with Windows 95/NT or higher Measured and calculated Poisson distribution Histogram: h(n), curve: N · wB (n) 226 P 6.4.2.1 1 1 1 1 1 1 1 2 2 1 Atomic and nuclear physics Radioactivity P 6.4.3 Radioactive decay and half-life P 6.4.3.3 Determining the half-life of Ba-137m – recording the decay curve using the digital counter P 6.4.3.4 Determining the half-life of Ba-137m – recording and evaluating the decay curve using CASSY Determining the half-life of Ba-137m – recording and evaluating the decay curve using CASSY (P 6.4.3.4) Cat. No. 559 815 559 01 575 48 524 010 524 200 524 033 664 043 664 103 300 02 300 42 301 01 666 555 Description Cs/Ba-137m isotope generator End-window counter Digital counter Sensor-CASSY CASSY Lab GM box Test tubes, 160 x 16 diam. Beaker, 250 ml, ss, hard glass Stand base, V-shape, 20 cm Stand rod, 47 cm Leybold multiclamp Universal clamp, 0 ... 80 mm dia. additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 For the activity of a radioactive sample, we can say: dN A(t) = dt P 6.4.3.3 P 6.4.3.4 { { 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 Here, N is the number of radioactive nuclei at time t. It is not possible to predict when an individual atomic nucleus will decay. However, from the fact that all nuclei decay with the same probability, it follows that over the time interval dt, the number of radioactive nuclei will decrease by dN = – Ö · N · dt Ö: decay constant Thus, for the number N, the law of radioactive decay applies: N(t) = N0 · e–Ö · t N0: number of radioactive nuclei at time t = 0 Among other things, this law states that after the half-life ln2 t1/2 = Ö the number of radioactive nuclei will be reduced by half. To determine the half-life of Ba-137m, a plastic bottle with Cs-137 stored at salt is used. The metastable isotop Ba-137 m arising from the b-decay is released by an eluation solution. The halftime amounts to 2.6 minutes approx. 227 Radioactivity P 6.4.4 Attenuation of R, T and H radiation P 6.4.4.1 Measuring the range of R radiation in air P 6.4.4.2 Attenuation of T radiation when passing through matter P 6.4.4.3 Confirming the law of distance for T radiation P 6.4.4.4 Absorption of H radiation when passing through matter Atomic and nuclear physics Absorption of H radiation when passing through matter (P 6.4.4.4) High-energy R and T particles release only a part of their energy when they collide with an absorber atom. For this reason, many collisions are required to brake a particle completely. Its range R E2 0 R“ n·Z depends on the initial energy E0, the number density n and the atomic number Z of the absorber atoms. Low-energy R and T particles or H radiation are braked to a certain fraction when passing through a specific absorber density dx, or are absorbed or scattered and thus disappear from the beam. As a result, the radiation intensity I decreases exponentially with the absorption distance x. I = I0 · e–B · x B: attenuation coefficient The first experiment determines the range R of monoenergetic R particles in air. Here, the ionization current I is measured in an ionization chamber of variable height as a function of the distance d between the cover and the Am-241 preparation. The ionization current initially increases with the distance d before remaining constant at distances which are greater than the range. The second experiment examines the attenuation of T radiation from Sr-90 in aluminum as a function of the absorber thickness d. This experiment shows an exponential decrease in the intensity. As a comparison, the absorber is removed in the third experiment and the distance between the T preparation and the counter tube is varied. As one might expect for a point-shaped radiation source, the following is a good approximation for the intensity: 1 I (d) “ 2 d The fourth experiment examines the attenuation of H radiation in matter. Here too, the decrease in intensity is a close approximation of an exponential function. The attenuation coefficient B depends on the absorber material and the H energy. 228 P 6.4.4.2 P 6.4.4.3 1 1 1 1 1 2 2 1 Cat. No. 559 82 546 25 546 27 546 35 521 70 532 00 575 24 531 100 311 52 300 02 300 41 301 01 666 555 500 610 501 40 501 45 559 83 559 18 559 01 575 471 Description Am 241 preparation Ionization chamber Telescopic cylinder Adapter for ionization chamber High voltage power supply 10 kV I-measuring amplifier D Screened BNC/4 mm Multimeter METRAmax 2 Vernier calipers, plastic Stand base, V-shape, 20 cm Stand rod, 25 cm Leybold multiclamp Universal clamp, 0...80 mm dia. Safety connecting lead, 25 cm, yellow/green Connecting lead, Ø 2.5 mm2, 25 cm, yellow/green Pair of cables, 50 cm, red and blue Set of 5 radioactive preparations Holder with absorber foils End-window counter for R, T, H and x-rays Counter S 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 590 02 591 21 532 16 300 11 460 97 Small clip plug Large clip plug Connection rod Saddle base Scaled metal rail, 0.5 m Geiger counter 1 1 2 2 667 9182 559 94 300 51 501 644 1 Set of absorbers and targets Stand rod, right angled Set of 6 two-way plug adapters, black 1 1 1 P 6.4.4.4 P 6.4.4.1 Atomic and nuclear physics Nuclear physics P 6.5.1 Demonstration of particle tracks P 6.5.1.1 Demonstrating the tracks of Rparticles in the Wilson cloud chamber Demonstrating the tracks of R-particles in the Wilson cloud chamber (P 6.5.1.1) Cat. No. 559 57 559 59 522 27 450 60 450 51 460 20 521 210 Description Wilson cloud chamber Radium source for Wilson cloud chamber Power supply 450 V DC Lamp housing Lamp, 6 V/30 W Aspherical condensor Transformer, 6 V AC,12 V AC/30 VA Bench clamp Saddle base Ethanol, fully denaturated, 1l Pair of cables, 1 m, red and blue 1 1 1 1 1 1 1 1 1 1 1 301 06 300 11 In a Wilson cloud chamber, a saturated mixture of air, water and alcohol vapor is briefly caused to assume a supersaturated state due to adiabatic expansion. The supersaturated vapor condenses rapidly around condensation seeds to form tiny mist droplets. Ions, which are formed e.g. through collisions of R particles and gas molecules in the cloud chamber, make particularly efficient condensations seeds. In this experiment, the tracks of R particles are observed in a Wilson cloud chamber. Each time the pump is vigorously pressed, these tracks are visible as traces of droplets in oblique light for one to two seconds. An electric field in the chamber clears the space of residual ions. 671 9720 501 46 Droplet traces in the Wilson cloud chamber P 6.5.1.1 229 Nuclear physics P 6.5.2 Rutherford scattering Atomic and nuclear physics P 6.5.2.1 Rutherford scattering: measuring the scattering rate as a function of the scattering angle and the atomic number Rutherford scattering: measuring the scattering rate as a function of the scattering angle and the atomic number (P 6.5.2.1) The fact that an atom is “mostly empty space” was confirmed by Rutherford, Geiger and Marsden in one of the most significant experiments in the history of physics. They caused a parallel beam of R particles to fall on an extremely thin sheet of gold leaf. They discovered that most of the R particles passed through the gold leaf virtually without deflection, and that only a few were deflected to a greater degree. From this, they concluded that atoms consist of a virtually massless extended shell, and a practically point-shaped massive nucleus. This experiment reproduces these observations using an Am-241 preparation in a vacuum chamber. The scattering rate N(P) is measured as a function of the scattering angle P using a GeigerMüller counter tube. As scattering materials, a sheet of gold leaf (Z = 80) and aluminum foil (Z = 13) are provided. The scattering rate confirms the relationship 1 N(P) “ and N(P) “ Z 2. sin4 P 2 Cat. No. Description 559 82 559 56 559 52 559 93 562 791 501 16 575 48 378 752 378 764 378 031 307 68 501 02 Am 241 preparation Rutherford scattering chamber Aluminum foil in holder Discriminator preamplifier Plug-in power unit Multicore cable, 6-pole, 1.5 m Digital counter Rotary-vane vacuum pump D 2.5 E Exhaust filter Small flange DN 16 KF with hose nozzle Vacuum tubing, 8/18 mm dia. BNC cable, 1 m long * additionally recommended 1 1 1 1 1 1 1 1 1 1 1 1 1* 1 1 2 1 1 1* 1 1 2 Scattering rate N as a function of the scattering angle P 230 P 6.5.2.1 (b) P 6.5.2.1 (a) Atomic and nuclear physics Nuclear physics P 6.5.3 Nuclear magnetic resonance (NMR) P 6.5.3.1 Nuclear magnetic resonance in polystyrene, glycerine and Teflon Nuclear magnetic resonance in polystyrene, glycerine and Teflon (P 6.5.3.1) Cat. No. Description NMR supply unit 514 602 514 606 562 11 562 131 521 545 575 294 1 1 1 2 1 1 NMR probe unit U-core with yoke Coil, 10 A, 480 turns DC power supply 0...16 V, 5 A Analog/digital oscilloscope HM 507 501 02 516 60 516 62 501 16 BNC cable, 1 m long Tangential B-probe Teslameter Multicore cable, 6-pole, 1.5 m long * additionally recommended 2 1* 1* 1* 500 621 500 641 500 642 I Safety connection lead, 100cm, red Safety connection lead, 50 I Safety connection lead, 100 cm, blue cm, red I I1 I1 I1 The magnetic moment of the nucleus entailed by the nuclear spin I assumes the energy states Em = – gl · BK · m · B with m = –I, –I + 1, . . . , I J BK = 5,051 · 10–27 : nuclear magneton T gI: g factor of nucleus in a magnetic field B. When a high-frequency magnetic field with the frequency V is applied perpendicularly to the first magnetic field, it excites transitions between the adjacent energy states when these fulfill the resonance condition h · V = Em+1 – Em h: Planck’s constant This fact is the basis for nuclear magnetic resonance, in which the resonance signal is detected using radio-frequency technology. For example, in a hydrogen nucleus the resonance frequency in a magnetic field of 1 T is about 42.5 MHz. The precise value depends on the chemical environment of the hydrogen atom, as in addition to the external magnetic field B the local internal field generated by atoms and nuclei in the near vicinity also acts on the hydrogen nucleus. The width of the resonance signal also depends on the structure of the substance under study. This experiment verifies nuclear magnetic resonance in polystyrene, glycerine and Teflon. The evaluation focuses on the position, width and intensity of the resonance lines. Diagram of resonance condition of hydrogen P 6.5.3.1 231 Nuclear physics P 6.5.4 R spectroscopy Atomic and nuclear physics P 6.5.4.1 R spectroscopy of radioactive samples P 6.5.4.2 Determining the energy loss of R radiation in air P 6.5.4.3 Determining the energy loss of R radiation in aluminum and in gold P 6.5.4.4 Determining the age of an Ra226 sample R spectroscopy of radioactive samples (P 6.5.4.1) Up until about 1930, the energy of R rays was characterized in terms of their range in air. For example, a particle of 5.3 MeV (Po-210) has a range of 3.84 cm. Today, R energy spectra can be studied more precisely using semiconductor detectors. These detect discrete lines which correspond to the discrete excitation levels of the emitting nuclei. The aim of the first experiment is to record and compare the R energy spectra of the two standard preparations Am-241 and Ra226. To improve the measuring accuracy, the measurement is conducted in a vacuum chamber. In the second experiment, the energy E of R particles is measured as a function of the air pressure p in the vacuum chamber. The measurement data is used to determine the energy per unit of distance dE /dx which the R particles lose in the air. Here, p x= · x0 p0 x0: actual distance, p0: standard pressure is the apparent distance between the preparation and the detector. The third experiment determines the amount of energy of R particles lost per unit of distance in gold and aluminum as the quotient of the change in the energy WE and the thickness Wx of the metal foils. In the final experiment, the individual values of the decay chain of Ra-226 leading to the R energy spectrum are analyzed to determine the age of the Ra-226 preparation used here. The activities A1 and A2 of the decay chain “preceding” and “following” the longer-life isotope Pb-210 are used to determine the age of the sample from the relationship –T I A2 = A1 · 1 – e P 6.5.4.3 1 1 1 1 1 1 1 1 1 1 1 1 1* 1 1 1 P 6.5.4.2 Cat. No. 559 82 559 430 559 56 559 52 559 93 524 010 524 058 524 200 501 16 501 02 501 01 575 211 378 752 378 764 307 68 378 031 378 045 378 050 378 015 378 776 378 510 Description Am 241 preparation Ra 226 preparation Rutherford scattering chamber Aluminium foil in holder Discriminator preamplifier Sensor-CASSY MCA Box CASSY Lab Multicore cable, 6-pole, 1.5 m BNC cable, 1 m BNC cable, 0.25 m Two-channel oscilloscope 303 Rotary-vane vacuum pump D 2.5 E Exhaust filter Vacuum tubing 8/18 mm Small flange DN 16 KF with hose nozzle Centering ring DN 16 KF Clamping ring DN 10/16 KF Cross DN 16 KF Metering valve DN 16 KF Pointer manometer 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1* 1 1* 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1* 1 1 4 4 1 1 1 1 1* 1 1 additionally required: 1 PC with Windows 95/NT or higher * additionally recommended 1 1 1 ( ) I = 22.3 a: lifetime of Pb-210 232 P 6.5.4.4 P 6.5.4.1 Atomic and nuclear physics Nuclear physics P 6.5.5 H spectroscopy P 6.5.5.1 Detecting H radiation with a scintillation counter P 6.5.5.2 Recording and calibrating a H spectrum P 6.5.5.3 Absorption of H radiation P 6.5.5.4 Identifying and determining the activity of weakly radioactive samples P 6.5.5.5 Recording a T spectrum using a scintillation counter Absorption of H radiation (P 6.5.5.3) Cat. No. 559 84 559 83 559 885 559 901 559 912 559 94 559 89 559 891 559 88 521 68 524 010 524 058 524 200 575 211 501 02 300 42 301 01 666 555 Description Mixed preparation R, T, H Set of 5 radioactive preparations Calibrating preparation 137 Cs, 5 kBq Scintillation counter Detector-output stage Set of absorbers and targets Scintillator screening Socket for scintillator Marinelli beaker High voltage power supply 1.5 kV Sensor-CASSY MCA Box CASSY Lab Two-channel oscilloscope 303 BNC cable, 1 m Stand rod, 47 cm Leybold multiclamp Universal clamp, 0...80 mm dia. Potassium chloride, 250 g additionally required: PC with Windows 95/NT or higher * additionally recommended 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1* 1* 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 672 5210 When interpreting H energy spectra recorded with a scintillation counter, it is necessary to take several interactive processes of the H radiation with the scintillator crystal into consideration. In the photoeffect, the H quanta transfer their entire energy to the crystal and are registered in the total absorption peak. Due to Compton scattering, it often occurs that only a part of the H energy is transferred to the crystal, as there is a certain probability that the scattered H quantum will exit the crystal. The H quanta are registered in a continuous distribution in which the upper and lower limits are determined by the maximum and minimum energy which can be transferred to the electron in Compton scattering. A third possible interaction, pair formation, is only significant at H energies above 2 MeV. In the first experiment, the output pulses of the scintillation counter are investigated using the oscilloscope and the multichannel analyzer MCA-CASSY. The total absorption peak and the Compton distribution are identified in the pulse-amplitude distribution generated with monoenergetic H radiation. The aim of the second experiment is to record and compare the H energy spectra of standard preparations. The total absorption peaks are used to calibrate the energy of the scintillation counter and to identify the preparations. The third experiment examines the attenuation of H radiation in various absorbers. The aim here is to show how the attenuation coefficient B depends on the absorber material and the H energy. A Marinelli beaker is used in the fourth experiment for quantitative measurements of weakly radioactive samples. This apparatus encloses the scintillator crystal virtually completely, ensuring a defined measurement geometry. Lead shielding considerably reduces the interfering background from the laboratory environment. The final experiment records the continuous spectrum of a pure T radiator (Sr-90/Y-90) using the scintillation counter. To determine the energy loss dE/dx of the T particles in aluminum, aluminum absorbers of various thicknesses x are placed in the beam path between the preparation and the detector. P 6.5.5.2 P 6.5.5.3 P 6.5.5.4 P 6.5.5.5 P 6.5.5.1 233 Nuclear physics P 6.5.6 Compton effect Atomic and nuclear physics P 6.5.6.1 Quantitative observation of the Compton effect Quantitative observation of the Compton effect (P 6.5.6.1) In the Compton effect, a photon transfers a part of its energy E0 and its linear momentum E p0 = 0 c c: speed of light in a vacuum to a free electron by means of elastic collision. Here, the laws of conservation of energy and momentum apply just as for the collision of two bodies in mechanics. The energy E0 E(P) = E0 1+ · (1 – cos P) m · c2 m: mass of electron at rest and the linear momentum E p= c of the scattered photon depend on the scattering angle P. The effective cross-section depends on the scattering angle and is described by the Klein-Nishina formula: p0 p dD 1 2 p2 + – sin2 P = · r0 · 2 · dE 2 p0 p p0 Cat. No. 559 800 559 809 559 84 559 901 559 912 521 68 524 010 524 058 524 200 Description Apparatus set Compton Cs-137 preparation, 3.7 MBq Mixed preparation alpha, beta, gamma Scintillation counter Detector output stage High voltage power supply 1.5 kV Sensor-CASSY MCA Box CASSY Lab additionally required: PC with Windows 95/NT or higher ( ) r0 = 2,5 · 10–15 m: classic electron radius In this experiment, the Compton scattering of H quanta with the energy E0 = 667 keV at the quasi-free electrons of an aluminum scattering body is investigated. For each scattering angle P, a calibrated scintillation counter records one H spectrum with and one without aluminum scatterer as a function of the respective scattering angle. The further evaluation utilizes the total absorption peak of the differential spectrum. The position of this peak gives us the energy E(P). Its integral counting rate N(P) is compared with the calculated effective cross-section. Measuring arrangement 234 P 6.5.6.1 1 1 1 1 1 1 1 1 1 1 Solid-state physics Table of contents Solid-state physics P7 Solid-state physics P 7.1 P 7.1.1 P 7.1.2 P 7.1.3 P 7.1.4 Properties of crystals Structure of crystals X-ray structural analysis X-ray structural analysis with the x-ray apparatus P Elastic and plastic deformation 237 238 239 240 P 7.3 P 7.3.1 P 7.3.2 Magnetism Dia-, para- und ferromagnetism Ferromagnetic hysteresis 247 248 P 7.4 P 7.4.1 Scanning probe microscopy Scanning tunneling microscope 249 P 7.2 P 7.2.1 P 7.2.2 P 7.2.3 P 7.2.4 P 7.2.5 P 7.2.6 Conduction phenomena Hall effect Electrical conduction in solid bodies Photoconductivity Luminescence Thermoelectricity Superconductivity 241 242 243 244 245 246 236 Solid-state physics Properties of crystals P 7.1.1 Structure of crystals P 7.1.1.1 Investigating the crystal structures of tungsten using a field emission microscope Investigating the crystal structures of tungsten using a field emission microscope (P 7.1.1.1) Cat. No. 554 60 554 605 301 339 521 70 521 39 531 712 500 614 500 624 500 641 500 642 500 644 Description Field emission microscope Connection plate FEM Pair of stand feet High voltage power supply 10 kV Variable extra low voltage transformer Ammeter, DC, I ≤ 10 A, e. g. Multimeter METRAmax 3 Safety connection lead, 25 cm, black Safety connection lead, 50 cm, black Safety connection lead, 100 cm, red Safety connection lead, 100 cm, blue Safety connection lead, 100 cm, black 1 1 1 1 1 1 2 2 1 1 2 In the field emission microscope, the extremely fine tip of a tungsten monocrystal is arranged in the center of a spherical luminescent screen. In the vicinity of the tip, the electric field between the crystal and the luminescent screen reaches such a high field strength that the conducting electrons can “tunnel” out of the crystal and travel radially to the luminescent screen. Here, an image of the emission distribution of the crystal tip is created, magnified by a factor of R V= r R = 5 cm: radius of luminescent screen r = 0,1-0,2 Bm: radius of tip In the first part of this experiment, the tungsten tip is purified by heating it to a white glow. The structure which appears on the luminescent screen after the electric field is applied corresponds to the body-centered cubic lattice of tungsten, which is observed in the (110) direction, i.e. the direction of one of the diagonals of a cube face. Finally, a minute quantity of barium is vaporized in the tube, so that individual barium atoms can precipitate on the tungsten tip to produce bright spots on the luminescent screen. When the tungsten tip is heated carefully, it is even possible to observe the thermal motion of the barium atoms. P 7.1.1.1 237 Properties of crystals P 7.1.2 X-ray structural analysis Solid-state physics P 7.1.2.1 P 7.1.2.2 P 7.1.2.3 P 7.1.2.4 Bragg reflection: determining the lattice constants of monocrystals Laue diagrams: investigating the lattice structure of monocrystals Debye-Scherrer photography: determining the lattice-plane spacings of polycrystalline powder samples Debye-Scherrer Scan: determining the lattice-plane spacings of polycrystalline powder samples Laue diagrams: investigating the lattice structure of monocrystals (P 7.1.2.2) When x-rays of the wavelength Ö are diffracted at a crystal, maxima occur at the reflection angles R, T, H which, when measured with respect to the crystal axes a, b, c, fulfill the Laue conditions h · Ö = a · (cos R0 – cos R), h = 0, ± 1, ± 2, ... k · Ö = b · (cos T0 – cos T), k = 0, ± 1, ± 2, ... l · Ö = c · (cos H0 – cos H), l = 0, ± 1, ± 2, ... R0, T0, H0: angle of incidence W. H. and W. L. Bragg described the behavior of x-rays in crystals in simplified terms as reflection at a set of parallel lattice planes. Reflection can only occur for the glancing angles P which fulfill the Bragg condition 2 · d · sin P = n · Ö with n = 1, 2, 3, . . . d: lattice plane spacing, n: diffraction order For a cubic lattice with the lattice constant a, the spacing of the lattice planes can be expressed using the Laue indices h, k, l: a d= 2 + k2 + l2 öh In the first experiment, the Bragg reflection of Mo-KR radiation (Ö = 71.080 pm) at NaCl and LiF monocrystals is used to determine the lattice constant. The KT component of the x-ray radiation can be suppressed using a zirconium filter. To make Laue diagrams at NaCl and LiF monocrystals, the bremsstrahlung radiation of the x-ray apparatus is used in the second experiment as “white” x-radiation. The positions of the “colored” reflections on an x-ray film behind the crystal and their intensities can be used to determine the crystal structure and the lengths of the crystal axes through application of the Laue condition. In the last two experiments, Debye-Scherrer photographs are produced by irradiating samples of a fine crystal powder with Mo-KR radiation. Among many unordered crytallites of the sample, the x-rays diffract at those which have an orientation conforming to the Bragg condition. The diffracted rays describe conical sections for which the aperture angles P can be derived 238 P 7.1.2.2 P 7.1.2.3 1 1 Cat. No. 554 811 559 01 554 77 554 842 554 838 Description X-ray apparatus End-window counter for a, b, g and x-rays LiF monocrystal for Bragg reflecion Set of 2 crystal powder-holder Film holder x-ray 1 1 1 1 1 554 896 554 87 554 88 667 091 667 092 311 54 X-ray film Agfa Dentus M2 LiF crystal for Laue diagrams NaCl crystal for Laue diagrams Pestle, porcelain, 100 mm, for 667 092 Mortar, porcelain, 63 mm dia. Precision vernier calipers additionally required: PC with Windows 95/NT or higher Developer for X-ray film Fixativer for X-ray film 1 1 1 1 1 1 1 1 554 897 554 898 I I I I1I1I I I1I1I Laue diagram of NaCl Debye-Scherrer photograph of NaCl from a photograph. This experiment determines the lattice spacing corresponding to P as well as its Laue indices h, k, l, and thus the lattice structure of the crystallite. P 7.1.2.4 1 1 1 1 1 P 7.1.2.1 1 Properties of crystals P 7.1.4 Elastic and plastic deformation P 7.1.4.1 Investigating the elastic and plastic extension of metal wires Solid-state physics Investigating the elastic and plastic extension of copper wires (P 7.1.4.1) The shape of a crystalline solid is altered when a force is applied. We speak of elastic behavior when the solid resumes its original form once the force ceases to act on it. When the force exceeds the elastic limit, the body is permanently deformed. This plastic behavior is caused by the migration of discontinuities in the crystal structure. In this experiment, the extension of iron and copper wires is investigated by hanging weights from them. A precision pointer indicator measures the change in length Ws, i. e. the extension Z= Ws s Cat. No. 550 35 550 51 342 61 340 911 381 331 340 82 314 04 301 07 301 01 301 25 301 26 301 27 300 44 Description Copper wire, 100 m, 0.20 mm dia. Iron wire, 100 m, 0.20 mm dia. Set of 12 weights, 50 g each Pulley, plug-in, 50 mm diameter Pointer for linear expansion Double scale Support clip, for plugging in Simple bench clamp Leybold multiclamp Clamping block MF Stand rod, 25 cm, 10 mm dia. Stand rod, 50 cm, 10 mm dia. Stand rod, 100 cm s: length of wire After each new tensile load D= F A F: weight of load pieces, A: wire cross-section the students observe whether the pointer returns to the zero position when the strain is relieved, i.e. whether the strain is below the elasticity limit DE. Graphing the measured values in a tension-extension diagram confirms the validity of Hooke's law D = E·Z E: modulus of elasticity up to a proportionality limit DP. Load-extension diagram for a typical metal wire 240 P 7.1.4.1 1 1 2 1 1 1 2 2 4 3 3 1 1 Solid-state physics Conduction phenomena P 7.2.1 Hall effect P 7.2.1.1 P 7.2.1.2 P 7.2.1.3 P 7.2.1.4 P 7.2.1.5 Investigating the Hall effect in silver Investigating the anomalous Hall effect in tungsten Determining the density and mobility of charge carriers in n-germanium Determining the density and mobility of charge carriers in p-germanium Determining the band gap of germanium Investigating the Hall effect in silver (P 7.2.1.1) Cat. No. 586 81 586 84 586 850 586 853 586 852 586 851 532 13 516 62 516 60 501 16 524 010 524 200 524 038 Description Hall effect apparatus, silver Hall effect apparatus, tungsten Base unit for Hall effect (Ge) n-Ge on plug-in board p-Ge on plug-in board Ge undoped on plug-in board Microvoltmeter Teslameter Tangential B-probe Multicore cable, 6-pole, 1.5 m long Sensor CASSY CASSY Lab B-box 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 In the case of electrical conductors or semiconductors within a magnetic field B, through which a current I is flowing perpendicular to the magnetic field, the Hall effect results in an electric potential difference 1 UH = RH · B · l · d d: thickness of sample The Hall coefficient 1 p · B2 – n · B2 p n RH = · e (p · B p + n · B n)2 e: elementary charge depends on the concentrations n and p of the electrons and holes as well as their mobilities Bn and Bp, and is thus a quantity which depends on the material and the temperature. The first two experiments determine the Hall coefficient RH of two electrical conductors by measuring the Hall voltage UH for various currents I as a function of the magnetic field B. A negative value is obtained for the Hall coefficient of silver, which indicates that the charge is being transported by electrons. A positive value is found as the Hall coefficient of tungsten. Consequently, the holes are mainly responsible for conduction in this metal. The third and fourth experiments explore the temperature-dependency of the Hall voltage and the electrical conductivity D = e · ( p · Bp + n · Bn) using doped germanium samples. The concentrations of the charge carriers and their mobilities are determined under the assuption that, depending on the doping, one of the concentrations n or p can be ignored. In the final experiment, the electrical conductivity of undoped germanium is measured as a function of the temperature to provide a comparison. The measurement data permits determination of the band gap between the valence band and the conduction band in germanium. P 7.2.1.2 P 7.2.1.3 P 7.2.1.4 2 1 1 1 2 1 1 1 7 1 521 55 521 39 521 50 521 545 High current power supply Variable extra low voltage transformer AC/DC power supply 0....15 V DC power supply 0....16 V, 5 A U-core with yoke Pair of bored pole pieces Coil with 250 turns Multimeter METRAmax 3 Stand rod, 25 cm Leybold multiclamp Stand base, V-shape, 20 cm Pair of cables, 1 m, red and blue Connecting lead, Ø 2.5 mm 2, 100 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 2 1 1 1 562 11 560 31 562 13 531 712 300 41 301 01 300 02 501 46 501 33 1 1 2 1 1 1 1 4 2 1 1 2 1 1 1 1 4 2 1 1 2 1 1 1 7 1 P 7.2.1.5 1 4 1 P 7.2.1.1 241 Conduction phenomena P 7.2.2 Electrical conduction in solid bodies P 7.2.2.1 Measuring the temperaturedependency of a noble metal resistor P 7.2.2.2 Measuring the temperaturedependency of a semiconductor resistor Solid-state physics Measuring the temperature-dependency of a noble metal resistor and a semiconductor resistor (P 7.2.2.1/ 2) The temperature-dependency of the specific resistance U is a simple test for models of electric conductivity of conductors and semiconductors. In electrical conductors, U increases with the temperature, as the collisions of the quasi-free electrons from the conduction band with the atoms of the conductor play an increasingly important role. In semiconductors, on the other hand, the specific resistance decreases as the temperature increases, as more and more electrons move from the valence band to the conduction band, thus contributing to the conductivity. These experiments measure the resistance values as a function of temperature using a Wheatstone bridge. The computer-assisted CASSY measured-value recording system is ideal for recording and evaluating the measurements. For the noble metal resistor, the relationship T U U = 240 K: Debye temperature of platinum R = RU · is verified with sufficient accuracy in the temperature range under study. For the semiconductor resistor, the evaluation reveals a dependency with the form R“e – WE 2kT Cat. No. Description 586 80 586 82 555 81 524 031 666 193 524 045 524 010 524 200 502 061 501 45 Noble metal resistor Semiconductor resistor Electric oven for 230 V Current supply box Temperature sensor NiCr-Ni Temperature box (NiCrNi/NTC) Sensor-CASSY CASSY Lab Safety connection box with ground Pair of cables, 50 cm, red and blue additionally required: PC with Windows 95/NT or higher 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 k = 1.38 · 10–23 J K : Boltzmann constant with the band spacing E = 0.48 eV. 242 P 7.2.2.2 P 7.2.2.1 Solid-state physics Conduction phenomena P 7.2.3 Photoconductivity P 7.2.3.1 Recording the current-voltage characteristic of a CdS photoresistor Recording the current-voltage characteristic of a CdS photoresistor (P 7.2.3.1) Cat. No. 578 02 460 21 450 60 450 51 521 210 Description STE photoresistor LDR 05 Holder for plug-in elements Lamp housing Lamp, 6 V/30 W Transformer, 6 V AC,12 V AC/30 VA Aspherical condensor Polarization filter Lens f = + 150 mm Precision optical bench, standardized cross section 1 m Optics rider, H = 90 mm/W = 50 mm Adjustable slit DC power supply 0....16 V, 5 A Digital-analog multimeter METRAHit 24 S Digital-analog multimeter METRAHit 26 S Connecting lead, 50 cm, blue Pair of cables, 100 cm, red and blue 1 1 1 1 1 1 2 1 1 6 1 1 1 1 1 2 460 20 472 401 460 08 460 32 460 352 460 14 521 545 531 281 531 301 500 422 501 46 Photoconductivity is the phenomenon in which the electrical conductivity D of a solid is increased through the absorption of light. In CdS, for example, the absorbed energy enables the transition of activator electrons to the conduction band and the reversal of the charges of traps, with the formation of electron holes in the valence band. When a voltage U is applied, a photocurrent Iph flows. The object of the experiment is to determine the relationship between the photocurrent Iph and the voltage U at a constant radiant flux Fe as well as between the photocurrent Iph and the radiant flux Fe at a constant voltage U in the CdS photoresistor. P 7.2.3.1 243 Solid-state physics Conduction phenomena P 7.2.5 Thermoelectricity P 7.2.5.1 Seebeck effect: Determining the thermoelectric voltage as a function of the temperature differential Seebeck effect: Determining the thermoelectric voltage as a function of the temperature differential (P 7.2.5.1) Cat. No. 557 01 590 011 532 13 382 34 666 767 664 104 Description Set of 3 simple thermocouples Clamping plug Microvoltmeter Thermometer, -10° to + 110 °C Hot plate, 150 mm dia., 1500 W Beaker, 400 ml, ss, hard glass 1 2 1 1 1 1 When two metal wires with different Fermi energies EF touch, electrons move from one to the other. The metal with the lower electronic work function WA emits electrons and becomes positive. The transfer does not stop until the contact voltage W – WA, 2 U = A, 1 e e: elementary charge is reached. If the wires are brought together in such a way that they touch at both ends, and if the two contact points have a temperature differential T = T1 – T2, an electrical potential, the thermoelectric voltage UT = U(T1) – U(T2), is generated. Here, the differential thermoelectric voltage dU R= T dT depends on the combination of the two metals. In this experiment, the thermoelectric voltage UT is measured as a function of the temperature differential T between the two contact points for thermocouples with the combinations iron/constantan, copper/constantan and chrome-nickel/constantan. One contact point is continuously maintained at room temperature, while the other is heated in a water bath. The differential thermoelectric voltage is determined by applying a best-fit straight line UT = R · T to the measured values. Thermoelectric voltage as a function of the temperature Top: chrome-nickel/constantan, Middle: iron/constantan, Bottom: cupper/constantan P 7.2.5.1 245 Conduction phenomena P 7.2.6 Superconductivity Solid-state physics P 7.2.6.1 Determining the transition temperature of a hightemperature superconductor P 7.2.6.2 Meißner-Ochsenfeld effect in a high-temperature superconductor Determining the transition temperature of a high-temperature superconductor (P 7.2.6.1) In 1986, K. A. Müller and J. G. Bednorz succeeded in demonstrating that the compound YBa2Cu3O7 becomes superconducting at temperatures far greater than any known up to that time. Since then, many high-temperature superconductors have been found which can be cooled to their transition temperature using liquid nitrogen. Like all superconductors, high-temperature superconductors have no electrical resistance and demonstrate the phenomenon known as the Meissner-Ochsenfeld effect, in which magnetic fields are displaced out of the superconducting body. The first experiment determines the transition temperature of the high-temperature superconductor YBa2Cu3O7-x. For this purpose, the substance is cooled to below its critical temperature of Tc = 92 K using liquid nitrogen. In a four-point measurement setup, the voltage drop across the sample is measured as a function of the sample temperature using the computer-assisted measured value recording system CASSY. In the second experiment, the superconductivity of the YBa2Cu3O7-x body is verified with the aid of the MeissnerOchsenfeld effect. A low-weight, high field-strength magnet placed on top of the sample begins to hover when the sample is cooled to below its critical temperature so that it becomes superconducting and displaces the magnetic field of the permanent magnet. Cat. No. 667 552 524 010 524 200 501 45 667 551 Description Experiment kit for determining transition temperature and electrical resistance Sensor-CASSY CASSY Lab Pair of cables, 50 cm, red and blue Experiment kit for Meissner-Ochsenfeld effect additionally required: PC with Windows 95/NT or higher 1 1 1 2 1 1 Meißner-Ochsenfeld effect in a high-temperature superconductor 246 P 7.2.6.2 P 7.2.6.1 Solid-state physics Magnetism P 7.3.1 Dia-, para- and ferromagnetism P 7.3.1.1 Dia-, para- and ferromagnetic materials in an inhomogeneous magnetic field Dia-, para- and ferromagnetic materials in an inhomogeneous magnetic field (P 7.3.1.1) Cat. No. 560 41 562 11 562 13 560 31 521 39 300 02 300 41 301 01 501 46 500 422 Description Apparatus for experiments on dia- and paramagnetism U-core with yoke Coil with 250 turns Pair of bored pole pieces Variable extra low voltage transformer Stand base, V-shape, 20 cm Stand rod, 25 cm Leybold multiclamp Pair of cables, 100 cm, red and blue Connecting lead, 50 cm, blue 1 1 2 1 1 1 2 1 1 1 Diamagnetism is the phenomenon in which an external magnetic field causes magnetization in a substance which is opposed to the applied magnetic field in accordance with Lenz's law. Thus, in an inhomogeneous magnetic field, a force acts on diamagnetic substances in the direction of decreasing magnetic field strength. Paramagnetic materials have permanent magnetic moments which are aligned by an external magnetic field. Magnetization occurs in the direction of the external field, so that these substances are attracted in the direction of increasing magnetic field strength. Ferromagnetic substances in magnetic fields assume a very high magnetization which is orders of magnitude greater than that of paramagnetic substances. In this experiment, three 9 mm long rods with different magnetic behaviors are suspended in a strongly inhomogeneous magnetic field so that they can easily rotate, allowing them to be attracted or repelled by the magnetic field depending on their respective magnetic property. Placement of a sample in the magnetic field P 7.3.1.1 247 Magnetism P 7.3.2 Ferromagnetic hysteresis Solid-state physics P 7.3.2.1 Recording the magnetization and hysteresis curves of a ferromagnet Recording the magnetization and hysteresis curves of a ferromagnet (P 7.3.2.1 a) In a ferromagnet, the magnetic induction B = Br · B0 · H Vs B0 = 4S · 10–7 : magnetic field constant Am reaches a saturation value Bs as the magnetic field H increases. The relative permiability Br of the ferromagnet depends on the magnetic field strength H, and also on the previous magnetic treatment of the ferromagnet. Thus, it is common to represent the magnetic induction B in the form of a hysteresis curve as a function of the rising and falling field strength H. The hysteresis curve differs from the magnetization curve, which begins at the origin of the coordinate system and can only be measured for completely demagnetized material. In this experiment, a current I1 in the primary coil of a transformer which increases (or decreases) linearly over time generates the magnetic field strength N H = 1 · I1 L L: effective length of iron core, N1: number of windings of primary coil. The corresponding magnetic induction value B is obtained through integration of the voltage U2 induced in the secondary coil of a transformer: 1 B= · ∫ U2 · dt N2 · A A: cross-section of iron core N2: Number of windings of secondary coil The computer-assisted measurement system CASSY is used to control the current and to record and evaluate the measured values. The aim of the experiment is to determine the relative permeability Br in the magnetization curve and the hysteresis curve as a function of the magnetic field strength H. Cat. No. Description 562 11 562 12 U-core with yoke Clamping device 1 1 2 1 562 14 522 621 Coil with 500 turns Function generator S 12, 0.1 Hz to 20 kHz 524 010 524 200 524 011 576 71 577 19 500 444 500 424 Sensor-CASSY CASSY Lab Power-CASSY Rastered socket panel section STE resistor 1 E, 2 W Connecting lead, 100 cm, black Connecting lead, 50 cm, black additionally required: PC with Windows 95/NT or higher 1 1 1 1 7 1 1 1 4 Recording the magnetization and hysteresis curves of a ferromagnet (P 7.3.2.1 b) 248 P 7.3.2.1 (b) 1 1 2 1 1 1 P 7.3.2.1 (a) Solid-state physics Scanning probe microscopy P 7.4.1 Scanning tunneling microscope P 7.4.1.1 Investigating a graphite surface using a scanning tunneling microscope Investigating a gold surface using a scanning tunneling microscope Investigating a MoS2 probe using a scanning tunneling microscope P 7.4.1.2 P 7.4.1.3 Investigating a graphite surface using a scanning tunneling microscope (P 7.4.1.1) Cat. No. Description 554 58 554 584 Scanning tunneling microscope MoS2 probe additionally required: PC with Windows 3.1 or Windows 95 1 1 1 1 1 The scanning tunneling microscope was developed in the 1980's by G. Binnig and H. Rohrer. It uses a fine metal tip as a local probe; the probe is brought so close to an electrically conductive sample that the electrons “tunnel” from the tip to the sample due to quantum-mechanical effects. When an electric field is applied between the tip and the sample, an electric current, the tunnel current, can flow. As the tunnel current varies exponentially with the distance, even an extremely minute change in distance of 0.01 nm results in a measurable change in the tunnel current. The tip is mounted on a platform which can be moved in all three spatial dimensions by means of piezoelectric control elements. The tip is scanned across the sample to measure its topography. A control circuit maintains the distance between tip and sample extremely precisely at a constant distance by maintaining a constant tunnel current value. The controlled motions performed during the scanning process are recorded and imaged using a computer. The image generated in this manner is a composite in which the sample topography and the electrical conductivity of the sample surface are superimposed. These experiments use a scanning tunneling microscope specially developed for practical experiments, which operates at standard air pressure. At the beginning of the experiment, a measuring tip is made from platinum wire. The graphite sample is prepared by tearing off a strip of tape. When the gold sample is handled carefully, it requires no cleaning; the same is valid for the MoS2 probe. The investigation of the samples begins with an overview scan. In the subsequent procedure, the step width of the measuring tip is reduced until the positions of the individual atoms of the sample with respect to each other are clearly visible in the image. P 7.4.1.1-2 P 7.4.1.3 249 Register Register A R radiation 228 R spectrum 232 aberration –, chromatic 173 –, lens 173 –, spherical 173 absorption edge 222–224 absorption spectrum 213 absorption – of H radiation 228, 233 – of light 178 – of microwaves 137 – of x-rays 222–224 AC power meter 118 acceleration 23–24 accumulator 165 AC-DC generator 123 action = reaction 27, 32 active power 132 activity determination 233 AD converter 166 adder 160, 164 additive color mixing 177 address bus 167-168 addressing 167 adiabatic exponent 83 aerodynamics 64–66 air resistance 65–66 airfoil 65, 66 ALU 167 Amontons' law 82 ampere, definition of 113 amplifier 157 amplitude hologram 186-187 amplitude modulation (AM) 135 AND 163–164 angle of inclination 121 angled projection 30 angular acceleration 33–34 angular velocity 33-34 anharmonic oscillation 43 annihilation radiation 233 anomalous Hall effect 241 anomalous Zeeman effect 220 anomaly of water 71 antenna 139 apparent power 132 Archimedes' principle 61 arithmetic and logic unit 165 arithmetic operation 168 arithmetic unit 165 astigmatism 173 astronomical telescope 174 asynchronous motor 125 atom, size of 205, 239 attenuation – of R, T and H radiation 228 – of x-rays 222, 224 autocollimation 172 T spectrum 233 Babinet's theorem 179 Balmer series 212 band gap 241 barrel aberration 173 beats 51, 57 bell 133 bending 13 bending radius 9 Bernoulli equation 66 Bessel method 172 Biot-Savart's law 114 bipolar transistors 156 biprism 182 birefringence 189, 191-192 black body 195 block and tackle 16 Bohr's magneton 219 Bohr's model of the atom 214–217 Boyle-Mariotte's law 82 Bragg reflection 223, 238–239 branches 168 Braun tube 143 break-away method 63 Breit-Rabi formula 220 bremsstrahlung 223–224 Brewster angle 188 bridge rectifier 156 brightness control 162 Brownian motion of molecules 81 buffer 165 building materials 69 buoyancy 61, 66 charge carrier concentration 241 charge distribution 100 charge transport 104 chromatic aberration 173 circular motion 31, 33–34 circular polarization 48, 189 circular waves 49 code converter 164 coder 164 coercive force 248 coil 127 collision 26–27, 32 color mixing 177 coma 173 combinatorial circuit 164 comparator 160 complementary colors 176 composition of forces 14 Compton effect 223, 234 computer-assisted experiments – in atomic and nuclear physics 224, 226-227 – in electricity 95, 113, 115, 117, 119 –121, 134, 139 – in electronics 153, 162 – in heat 76, 79, 87 – in mechanics 12, 24–27, 29, 35, 41, 43–44, 51–52, 54–55, 57, 59, 64–66 – in optics 180 –181, 194-195, 201 – in solid-state physics 239, 241, 242, 246, 248 condensation heat 78 conductivity 241–242 conductor, electric 100, 105 –107, 242 – 243 conoscopic ray path 192 conservation of angular momentum 35 conservation of energy 26–27, 32, 35 conservation of linear momentum 26–27, 32 constant-current source 151 constant-voltage source 151 control bus 168 control, closed-loop 162 control, open-loop 161 cork-powder method 53 Coulomb's law 93-95 counter 164 counter tube 225 counting rates, determination of 226 coupled pendulums 44 coupling of oscillations 44– 45 Cp, CV 83 CPU timer 167 crest factor 132 critical point 80 critical potentials 217 cross grating 179 crystal lattice 237-239 current source 151–152 current transformation of a transformer 119 curve form factor 130 cushion aberration 173 cW value 65 C calcite 189 caliper gauge 9 canal rays 147 capacitance – of a plate capacitor 102–103 – of a sphere 101 capacitive impedance 126, 128–129 capacitor 102–103, 126 cathode rays 147 Cavendish hemispheres 100 center of gravity 31 central force 31 central processing unit 167 centrifugal and centripetal force 36–37 chaotic oscillation 43 characteristic radiation 223–224 characteristic(s) – of a diode 155 – of a field-effect transistor 156 – of a glow lamp 153 – of a light-emitting diode 155 – of a photoresistor 243 – of a phototransistor 158 – of a solar battery 152 – of a transistor 156 – of a tube diode 140 – of a tube triode 141 – of a varistor 153 – of a Z-diode 155 charge, electric 91-95, 140–144 B T radiation 228 252 Register D DA converter 166 damped oscillation 42–43 Daniell element 110 data bus 167–168 data transfer 168 de Broglie wavelength 210 de Morgan's laws 163 Debye temperature 242 Debye-Scherrer diffraction of electrons 210 Debye-Scherrer photograph 238 decimeter waves 135–136 decoder 164 decomposition of forces 14 decomposition of white light 176 deflection of electrons – in an electric field 143 –144 – in a magnetic field 142 –144 demultiplexer 164 density balance 10 density maximum of water 71 density –, measuring 10 – of liquids 10 – of solids 10 – of air 10 detection – of radioactivity 225 – of x-rays 221, 224 diamagnetism 247 dielectric constant 102–103 – of water 135 differentiator 160 diffraction – at a crossed grating 179 – at a double slit 50, 57, 137, 179 –181 – at a grating 50, 57, 179 – at a half-plane 181 – at a multiple grating 50, 57, 179 –181 – at a pinhole diaphragm 179 – at a post 179 – at a single slit 50, 57, 137, 179 –181 diffraction – of electrons 210 – of light 179 –181 – of microwaves 137 – of ultrasonic waves 57 – of water waves 50 – of x-rays 223 digital control systems 66 diode 140, 155 –156 diode characteristic 140, 155 directional characteristic 135 – of antennas 139 dispersion – of liquids 175 – of gases 175 distortion 173 doping 241 doppler effect 49, 58 dosimetry 221, 224 double mirror 182 double pendulum 44 double slit, diffraction at 50, 57, 137, 179 –181 dualism of wave and particle 210 Duane and Hunt's law 223 dynamic pressure 64 E e, determination of 206 e/m, determination of 144, 207 Earth inductor 121 Earth's magnetic field 121 echo sounder 56 eddy currents 118 edge absorption 223 edge, diffraction at 181 Edison effect 140 efficiency – of a heat pump 88 – of a hot air engine 86 – of a solar collector 73 – of a transformer 120 elastic collision 26–27, 32 elastic deformation 240 elastic strain constant 13 elastic torsion collision 35 electric charge 91– 95, 100, 140 –144 electric conductor 100, 105 –107, 242–243 electric current as charge transport 104 electric energy 77, 131 –132 electric field 96–97 electric generator 123, 125 electric motor 124-125 electric oscillator circuit 59, 128 electric power 131–132 electric work 131–132 electrical machines 122 –125 electrochemistry 110 electrolysis 109 electromagnet 111, 122 electromagnetic oscillations 59, 134 electromechanical devices 133 electrometer 91–92 electron charge 206 electron diffraction 210 electron holes 241, 243 electron spin 218-220 electron spin resonance 218 electrostatic induction 91– 92, 100 electrostatics 91– 92 elliptical polarization 189 emission spectrum 213 energy loss of a radiation 232 energy spectrum of x-rays 223–224 energy –, electrical 77, 131–132 –, heat 76–77 –, mechanical 16–17, 24–27, 32, 35, 76 energy-band interval 241 equilibrium 15 equilibrium of angular momentum 15 ESR see electron spin resonance evaporation heat 78 excitation energies 217 excitation of atoms 214 –217 expansion 69 Faraday cylinder 100 Faraday effect 193 feedback 134 ferromagnetism 247–248 field effect transistor 156, 157 field emission microscope 237 fine beam tube 207 fine crystal structure 223 fixed pulley 16 flip-flop 164 fluorescence 244 fluorescent screen 221 focal point, focal length 172 force 13–18, 21 –, measuring on current-carrying conductors 113 – along the plane 17 – in an electric field 98–99 – normal to the plane 17 forced oscillation 42–43 Foucault-Michelson method 196 Fourier transformation 59 Franck-Hertz experiment 215–216 free fall 28–30 frequency 40–53, 56-59, 134–135, 137 frequency modulation (FM) 135 frequency response 130 Fresnel biprism 182 Fresnel's laws 188 Fresnel's mirror 182 friction 18 friction coefficient 18 full-wave rectifier 156 G H radiation 228 H spectrum 233 Galilean telescope 174 galvanic element 110 gas discharge 145-146 gas elastic resonance apparatus 83 gas laws 82 gas thermometer 82 Gay-Lussac's law 82 Geiger counter 225 Geiger-Müller counter tube 225 generator circuits 157 generator, electric 123, 125 geometrical optics 171–174 glowing layer 146 golden rule of mechanics 16–17 Graetz circuit 155 grating spectrometer 200, 201 grating, diffraction at 50, 57, 179 gravitation torsion balance after Cavendish 11–12 Gravitational acceleration 28-29, 40 Gravitational constant 11–12 Gyroscope 38 F Falling-ball viscosimeter 62 Faraday constant 109 H h, determination of 208–209, 233 half-life 126 –127, 227 253 Register half-plane, diffraction at 181 half-shadow polarimeter 190 half-wave rectifier 156 Ha-line 212 Hall effect 241 hammer interrupter 133 harmonic oscillation 41–43 heat capacity 75 heat conduction 72 heat energy 76–77 heat engine 84, 86–87 heat equivalent –, electric 77 –, mechanical 76 heat insulation 72 heat pump 85–86, 88 helical spring 13, 41 helical spring after Wilberforce 45 helical spring waves 46 Helmholtz coils 114 high voltage 120 high-temperature superconductor 246 hologram 186 –187 homogeneous electric field 98 Hooke's law 13, 240 hot-air engine 84–87 Huygens' principle 49 hydrostatic pressure 60 hyperfine structure 220 hysteresis 248 J jump instructions 167 jumps 168 K KR-line 223–224 K-edge 222– 224 Keplerian telescope 174 Kerr effect 191 kinetic energy 24 –25 kinetic theory of gases 81– 83 Kirchhoff's laws 106 –107 Kirchhoff's law of radiation 195 Kirchhoff's voltage balance 99 Klein-Nishina formula 234 Kundt's tube 53 L Lambert's law of radiation 194 latch 165 latent heat 78 Laue diagram 238 law of distance 224, 228 laws of images 172 laws of radiation 195 leaf spring 13 Lecher line 136, 138 LED 154 –155 length measurement 9 Leslie's cube 195 lever 15 lever with unequal sides 15 light emitting diode 154 –155 light waveguide 158 light, velocity of 196 –198 line spectrum 199 –200, 212–213 linear motion 19–25 lines of force 96, 111 lines of magnetic force 111 Lloyd's experiment 50, 182 logical operations 163 –165 longitudinal waves 46 loose pulley 16 luminescence 244 luminous zone 146 Lummer-Gehrcke plate 219 I I/O elements 167 ideal gas 82 illuminance 194 image charge 99, 101 imaging aberrations 173 impedance 126 –128 inclined plane 17, 31 independence principle 30 –31 induction 115–117, 122 inductive impedance 127–129 inelastic collision 26–27, 32 inelastic electron collision 214–217 inelastic rotational collision 35 integrator 160 interference – of light 182 – of ultrasonic waves 57 – of water waves 50 interferometer 184 –185 internal resistance 108, 151 –152 interrupt 168 intrinsic conduction 241 inverting operational amplifier 160 ion dose rate 221 ion trap 211 ionization chamber 221, 225 ionization energy 217 ionizing radiation 225 IR position detector 12 irradiance 194 isoelectric lines 97 Malus' law 188 mathematical pendulum 40 Maxwell measuring bridge 129 measuring bridge –, Maxwell 129 –, Wheatstone 106-107 –, Wien 129 measuring range, expanding 108 mechanical energy 16 –17, 24 –27, 32, 35, 76 Meissner-Ochsenfeld effect 246 Melde's law 48 melting heat 78 metallic conductor 242 Michelson interferometer 184 micrometer screw 9 microprocessor 168 microscope 174 microwaves 137–138 Millikan experiment 206 mixing temperature 74 mobility of charge carriers 241 modulation of light 192 modulus of elasticity 13 Mohr density balance 10 molecular motion 81 molecule, size of 205 Mollier diagram 88 moment of inertia 38–39 Moseley's law 223-224 motions –, one-dimensional 19–25 –, two-dimensional 31–32 –, uniform 19–25, 33–34 –, uniformly accelerated 19 –25, 33–34 – with reversal of direction 23–25 motor, electric 124 –125 multimeter 130 multiple slit, diffraction at 50, 57, 179 –181 multiplexer 164 N NAND 163 –164 n-doped germanium 241 Newton rings 183 Newton, definition of 21 Newton's experiments with white light 176 Newton's law 32 NMR see nuclear magnetic resonance non-inverting operational amplifier 160 non-self-maintained gas discharge 145 NOR 163 –164 normal Hall effect 241 normal Zeeman effect 219 NOT 163 NTC resistor 153 nuclear magnetic resonance 231 nuclear magneton 220 nuclear spin 220, 231 nutation 38 M machine(s) –, simple 16 –17 –, electrical 122–125 Mach-Zehnder-Interferometer 185 magnetic field of a coil 114 magnetic field of Helmholtz coils 114 magnetic field the Earth 121 magnetic focusing 142 magnetic moment 112 magnetization curve 248 magnets 111,122 magnifier 174 Maltese-cross tube 142 O ohmic resistance 105 –108 Ohm's law 105 oil spot experiment 205 254 Register one-sided lever 15 operational amplifier 159 –160 opposing force 32 optical activity 190 optical analogon 210 optical pumping 220 optical transmission line 158 optoelectronics 158 OR 163 –164 orbital spin 219–220 oscillation of a string 52 oscillation period 40–45, 83, 134 oscillations 40–45, 52, 59, 134 oscillator 157 oscillator circuit 59, 128 prism spectrometer 199 program counter 168 program memory 167 projection parabola 30 propagation velocity – of voltage pulses 197 – of waves 47–49 propagation – of electrons 142 – of water waves 49 PTC resistor 153 pV diagram 84 – 85, 87 pyknometer 10 rotor 122 –125 Rutherford scattering 230 Rydberg constant 223 S saccharimeter 190 scanning tunneling microscope 249 scattering of H quanta 234 scintillation counter 233 Seebeck effect 245 self-excited generator 123 self-maintained gas discharge 145 –146 semiconductor detector 232 semiconductors 242 sequential circuit 164 series connection – of capacitors 102 – of resistors 106 servo control 162 shift instructions 168 shift register 164 simple machines 16 –17 single slit, diffraction at 50, 57, 137, 179 –181 slide gauge 9 sliding friction 18 slit, diffraction at 50, 57, 137, 179 –181 Snellius' law 49, 171 sodium D-lines 200 solar battery 152 solar collector 73 sound 59 sound waves 51, 53 –55 sound, velocity of – in air 54 – in gases 54 – in solids 55 special resistors 153 specific conductivity 242 specific electron charge 144, 207, 219 specific heat 75 specific resistance 105, 242 spectrometer 199 spectrum 199, 212 speech analysis 59 spherical aberration 173 spherometer 9 spin 218 –220, 231 spring 13 spring pendulum 41 standard potentials 110 standing wave 46, 50, 53, 136 –138 standing waves 138 static friction 17–18 static pressure 64 stator 122–125 Stefan-Boltzmann's law 195 Steiner's law 39 Stirling process 84-87 storage addresses 168 straight waves 49 subprogram call 168 subtractive color mixing 177 subtractor 160 Q quantum nature 186, 188–189, 195–197 quantum nature of charges 206 quartz, right-handed and left-handed polarization 190 P parallel connection – of capacitors 102 – of resistors 106 parallelogram of forces 14 paramagnetism 247 particle tracks 229 path-time diagram 19 –25, 33 –34 Paul trap 211 S-doped germanium 241 peak voltage 132 pendulums –, coupled 44 –, mathematical and physical 40 performance number 88 permanent magnets 111, 122 Perrin tube 143 phase hologram 186 –187 phase transition 78 –80 phase velocity 46 –49 phosphorescence 244 photoconductivity 243 photodiode 158 photoelectric effect 208 –209 photoresistor 153, 243 phototransistor 158 physical pendulum 40 PID controller 162 pinhole diaphragm, diffraction at 179 Planck's constant 208 –209, 223 plastic deformation 240 plate capacitor 102 –103 Pockels effect 192 Poisson distribution 226 polarimeter 190 polarity of electrons 143 polarization – of decimeter waves 135 – of light 188-193 – of microwaves 137 post, diffraction at 179 potentiometer 106 power plant generator 123 power transformation of a transformer 120 precession 38 pressure 60 primary colors 177 R radioactive dating 232 radioactive decay 227 radioactivity 225 –226 RAM 167 range of a radiation 228 reactance 126 –128 reactive power 132 real gas 80 recoil 26 rectification 140, 155 redox pairs 110 reflection –, law of 49, 56, 171 – of light 171 – of microwaves 137 – of ultrasonic waves 56 – of water waves 49 refraction –, law of 49, 171 – of light 171 – of microwaves 137 – of water waves 49 refractive index 49, 175, 185, 188, 198 refrigerating machine 85 register 164 –165 relay 133 remanence 48 resistors, special 153 resonance 2, 128 resonance absorption 218, 220 reversing pendulum 40 revolving-armature generator 123, 125 revolving-field generator 123, 125 rigid body 31-32 RMS voltage 132 rocket principle 26 rolling friction 18 rotating the plane of polarization 190, 193 rotating-crystal method 239 rotating-mirror method 196 rotation instructions 168 rotational motion 31–34 rotational oscillation 42– 43 255 Register subtractor unit 165 sugar solution, concentration of 190 superconductivity 246 superpositioning principle 30 –31 surface tension 63 synchronous motor 124 –125 transversal waves 46 triode 141 tube diode 140 tube triode 141 tuning fork 51 two-beam interference 50, 57 two-dimensional motion 31– 32 two-pole rotor 124 two-pronged lightning rod 120 two-quantum transitions 220 two-sided lever 15 Tyndall effect 188 volumetric expansion coefficient 69 –70 vowel analysis 59 W Waltenhofen's pendulum 118 water 71, 135 water waves 49-50 wave machine 47 waveguide 138 wavelength 46-49, 52-53, 184 waves 46–59, 135 –139, 179 –187 Wheatstone measuring bridge 106 –107 wheel and axle 15 white light 176 white light reflection hologram 186 Wien measuring bridge 129 Wilson cloud chamber 229 wind speed 64 wind tunnel 66 work –, electrical 77, 84–87, 131–132 –, mechanical 16 –17, 24 –25, 76, 84–87 T tachymeter 21 telescope 174 temperature 74 temperature variations 72 terrestrial telescope 174 thermal emission in a vacuum 143 thermal expansion – of liquids 70 – of solid bodies 69 – of water 71 thermodynamic cycle 84–88 thermoelectric voltage 245 thermoelectricity 45 Thomson tube 144 thread waves 46, 48 three-phase generator 125 three-phase machine 125 three-pole rotor 124 time constant – L/R 127 – RC 126 torsion balance 93 torsion collision 35 total pressure 64 total reflection of microwaves 137 traffic-light control system 161 transformer 119 –120 transformer under load 119 transistor 156 –157 transit time measurement 197 transition temperature 246 translational motion 31-32 transmission hologram 187 transmission of filters 201 transmitter 135, 137 U ultrasonic waves 56 –58 uniform acceleration 19 –25, 31, 33–34 uniform motion 19 –25, 31, 33 –34 universal motor 124 V vapor pressure 79 velocity 19 –25 velocity filter for electrons 144 Venturi tube 64 Verdet's constant 193 vernier 9 VideoCom 25, 27, 29, 44, 181, 201 viscosity 62 voltage amplification with a tube triode 141 voltage balance 99 voltage control 162 voltage divider 106 voltage optics 189 voltage pulse 115 voltage series 110 voltage source 151 –152 voltage transformation in a transformer 119 volume flow 64 volume measurement 10 volumetric expansion 70 X XOR 163 X-ray photography 221, 224 X-ray structural analysis 238–239 X-rays 221–224, 238–239 Y Young's experiment 50, 57, 137, 179 –181 Z Z-diode 154–155 Zeeman effect 219–220 Zero page 168 256