in the waveguide, and has the property of allowing current to flow along
in one polarity, but not in the other; it thus generates a pulsating direct
current which is rectified and then displayed with the meter on the reciever
unit.Many phenomena whose study comes under the heading of "physical optics" arise from certain integral relationships between the wavelength of the radiation and dimensions of the experimental apparatus. Since a part of this experiment and all of Experiment 5 involve such ratios, these studies will be done with microwaves, i.e., very short radio waves having wavelengths of a few centimeters, rather than with visible light, where changes of system dimensions over a few wavelengths are very difficult to produce and control, and quite impossible to see directly.
Purpose
To study reflection and refraction of electromagnetic waves; to measure the index of refraction of various materials; and to determine the wavelength of the microwaves used in this study.
Equipment
Background
Your basic equipment consists of a microwave generator (or transmitter), and a receiver. The transmitter consists of a Gunn-effect oscillator, a short piece of rectangular channel called a waveguide, which conducts the wave energy from one point to another, and a horn antenna, which directs the radiation into a fairly narrow beam in a selected direction.
The receiver gathers wave energy from a certain area over the wave fronts by
means of its horn antenna and directs that wave energy into a short waveguide
section containing a crystal rectifier. The rectifier is aligned along the
electric vector
in the waveguide, and has the property of allowing current to flow along
in one polarity, but not in the other; it thus generates a pulsating direct
current which is rectified and then displayed with the meter on the reciever
unit.
The transmitter and receiver are mounted at the ends of two arms which rotate about a center stage. Since much of what you will study and measure concerns the change in ray direction caused by some physical process, the stage is provided with an angular scale. The process of interest will occur on the central stage.
A. Measure the free-space wavelength, 
0
The manufacturer specifies the frequency of the microwaves to be 10.525 Ghz (1 Ghz = 109 Hz.)
Compute the corresponding wavelength and set up a reflector an integral number of 1/2 wavelengths away from the transmitter so as to produce a standing wave. The optimal distance from source to reflector will produce the largest ratio between measurements at node and anti-nodes. Use the detector probe to measure the distance between nodes (minimal field) and anti-node (maximal field). The receiver should not be used to measure the standing wave pattern because the horn would seriously alter the pattern. The small detector probe cable should be plugged into the receiver and the receiver horn pointed away from the transmitter.
When you compute the wavelength you will find that is is relatively short. Give some thought to what procedure will provide the best accuracy. For example, would it be better to measure the distances between successive minima and average them or to measure the distance between pairs of minima separated by several wavelengths? How well does the specified frequency (wavelength) agree with your measurements?
Hints:
B. Determine the index of refraction
Using a single solid prism, arrange the transmitter beam to be incident perpendicular to one of the prism faces so that no bending (refraction) of the beam will occur until it strikes the second surface and passes out of the prism. Determine the index of refraction by measuring the refraction angle of the beam as it emerges from the prism.
Hints:
) of the microwave beam without moving the transmitter. The
fact that the beam should be deflected the same amount, but in the opposite
direction, will cause many systematic errors to cancel if the average of the
magnitudes of the two deflection angles are used with Snell's law to find n.
This double measurement approach will also help verify that you are using the
correct out going beam. The "diffractive" nature of the microwave transmitter
beam leads to something like three beams emerging from the prism. Only the
highest intensity reading should be used, and it should be at about the same
deflection angle (on each side) for the two symmetric geometries.
C. Measure the Wavelength (within the material)
Construct a slab of variable thickness by using two solid prisms as shown in
Figure 6. By observing the variations in reflected intensity with slab
thickness, find the wavelength, , of the microwaves in the material. A
graph of n vs. d for maxima (or n+ 1/2 vs. d for minima) can be used to obtain
the wavelength, as well as the phase shift (by extrapolating to d = 0 )
between the reflections at the outer and inner surfaces.
Combine this result with the measurement of n (in part B) to find the free
space wavelength, 0, and the frequency of the microwaves you
are using. Compare this value of 0 with the direct
measurement of 0 in air (part A). Include the experimental
uncertainties in your measurements and indicate their origin.
D. Pellet-Filled Prism (optional)
Measure the index of refraction of the Pellet-filled foam prism using similar techniques. An "empty" foam prism can be used to check for systematic errors.
A note on error analysis:
For the non-linear function,
F() = A sin ,
we have for the error in F
F =
= A cos
and for the fractional error in F
F =
=
where the uncertainty in , , is expressed in radians.