Interference and Diffraction of Microwaves References: Equipment: Ford, Kenneth W., Classical and Modern Physics Vol2 Xerox College Publishing 1972 pp. 850-871. Pasco Instruction Manual and Experiment Guide for Microwave Optics (WA-9314B) Cenco Microwave Optics Demonstration Apparatus Manual a) Pasco Microwave Transmitters,Receivers and Accessories (λ = 2.9 cm) b) Cenco Microwave Transmitters, Receivers, and Accessories (λ 10 cm) Introduction: The classical experiments of Young, Fresnel, and the others in the early 1800 s, which did so much to establish the wave theory of light, are on almost a macroscopic scale, because of 5 the small wavelength of light ( 5 10 cm). Similar experiments can be done on a much larger scale, and therefore more easily, using microwaves, which are electromagnetic wavelengths on the order of 1-50 centimeters. The sources in our laboratory are small electronic generators of approximately 2.9 cm (Pasco) or 10 cm waves (Cenco), feeding a miniature antenna in a metal reflector bowl. The receiver or detector of the waves is a similar antenna connected to a microammeter through a rectifier. Either a metal screen or a plate of metal makes a good mirror for these microwaves. A partly transparent mirror, the equivalent of a half-silvered mirror in light optics, can be made from a sufficiently coarse screen. With such simple apparatus a number of basic experiments can be performed which demonstrate the interference and diffraction of electromagnetic waves. Study each of the following experiments or phenomena in your textbook or an equivalent source before coming to the laboratory. 140519 1
Theory: The microwaves studied in these experiments satisfy Maxwell s equations in free space. They reduce to two wave equations for the electric and magnetic field vectors (MKS units). 2 E 2 E z μ!ε 2! t = 0 2 (1) 2 B 2 B z μ!ε 2! t = 0 2 (2) Correct interpretation of the solution of these equations show that the waves propagate with a speed given by: c = 1 μ! ε! 3.0 10! m/s (3) where μ! and ε! are the permeability and permitivity constants (MKS). One can easily verify that the following sinusoidal solutions satisfy Equations 1 and 2. E! = E! sin 2π z ct λ (4) B! = B! sin 2π z ct λ (5) 140519 2
where B! = E! /c (6) The solution shows that the electric and magnetic fields are perpendicular to each other and to the direction of propagation (we have chosen the z direction as the propagation direction). In many of the experiments described below you will be able to measure the wavelength λ of these waves. Procedure: Michelson Interferometer: 1. Using a half-silvered mirror and full mirrors set up a Michelson interferometer. Adjust the mirrors carefully so as to obtain the maximum difference between full constructive and full destructive interference. Make a careful measurement of the wavelength of the microwaves. Standing Waves: 2. Knowing the wavelength set up the source, detector and mirrors so as to produce the standing waves. Adjust the apparatus to obtain the maximum effect and again determine the wavelength. Lloyd Mirror: 3. The interference will be observed between the waves which travel directly from the source to the detector and the waves that bounce off a mirror placed parallel to and on the side of the direct path. Move the mirror away from the direct path and observe the interference effect in the detector. Measurements made here should also be used to calculate the wavelength of the radiation. Diffraction: 4. The spreading of waves passes through a slit is called diffraction. Observe the diffraction pattern (the intensity variation) of radiation that passes through a single slit. Make observations for three slit widths: (a) very much larger than the wavelength, (b) about twice as large, and (c) approximately equal to the wavelength. 140519 3
Double-slit Interference Pattern: 5. Perform the microwave equivalent of Young s double slit experiment. Make observations in which the distance between the two slits is varied. From the geometry and observed intensity patterns, again deduce the wavelength. 140519 4
Cenco Equipment List Filled Out By: Date: Equipment Needed Experiment Name: INTERFERENCE AND DIFFRACTION OF MICROWAVES No. of Complete Setups PERMANENT ITEMS: Room No., No. Needed Total Cabinet No., Name, Brand, Description of Item per setup No. Needed Shelf MICROWAVE TRANSMITER 2 117 C-2 MICROWAVE RECEIVER 2 117 C-2 MIRROR (WINDOW SCREEN) 2 136 MIRROR (1/2 SCREEN) 1 136 GRATING (APPARATUS(FOR MICROWAVE) 1 136 METER STICK- 2 METER 2 144 WALL EXPENDABLE ITEMS: MISCELLANEOUS ITEMS, COMMENTS: 140519 5