Physics 21330 Spring 2010
Experiment 1
MICROWAVE OPTICS
I.
Introduction:
In this experiment, you will use microwaves of wavelength 2.8 cm to study geometrical and physical
optics for electromagnetic waves other than visible light. Some of the phenomena you will study are
ones you have already observed using waves of shorter wavelength, i.e., visible light. By using
waves whose wavelength is on the order of the diameter of one of your fingers, you will find that the
transverse wave nature of electromagnetic waves can easily be observed. Ordinary geometrical
optics phenomena such as transmission, absorption, reflection, total internal reflection, etc., can be
observed and compared with your previous observations using visible light. You will study the
transverse wave nature of microwaves and how they are transmitted or absorbed, and totally or
partially reflected by various objects. Then you will directly measure the wavelength of the waves
by making measurements on a standing wave pattern set up by reflection. Finally, you will perform
Young’s two-slit interference experiment, then cover one of the slits and observe the resulting
diffraction pattern.
You will observe that microwaves interact significantly with parts of your body, so you should be
careful to keep yourself as much as possible away from the region where the microwave radiation is
present in order to minimize the effects on your results. In particular, do not stand too close to the
microwave transmitter and/or receiver when making measurements or the radiation reflected or
refracted by your body may affect the intensity of the radiation arriving at the receiver. Note that the
power radiated by the transmitter is very much too small to produce significant health effects (unlike
microwave ovens). However, it is best not to look directly into the microwave transmitter while it is
operating.
II.
Required Equipment:
Microwave transmitter (orange), two Pasco (gray with meters) receivers (wavelength  = 2.8 cm),
microwave probe (small receiver), D.C. power supply, support stands or cradles, meter stick, tape
measure, metal plate, board, metal grid, two paraffin block prisms, double-slit assembly with
protractor and 60-cm long arm, probe stand.
III.
Procedure:
A.
Transmission, Reflection, and Absorption
1) Connect the power supply to the (orange). Position the transmitter and one receiver on support
stands or cradles with the horns facing each other about 50 to 80 cm apart. Line them up along
the side of the meter stick. Rotate them both until the electric fields radiated by the transmitter
and detected by the receiver are vertical (The terminals on the back of the transmitter should
form a horizontal line. Look inside the waveguide horn; the E-field is parallel to the dipole, the
small rod inside the rectangular wave guide at the base of the horn, which should now be
vertical. The meter on the Pasco receiver will be on top.) Turn on the receivers and/or meters
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and set the Pasco meters on 30x initially. You may need to change the range for different parts
of the experiment. Turn on the power supply and apply about 8 to 10 V to the (orange)
transmitter. (BE CAREFUL! NEVER apply voltage to a receiver!). The meter for the receiver
should show a good signal. Change ranges if necessary. Try varying the positions and pointing
directions of the transmitter and receiver and observe the changes in the size of the signal
detected by the receiver. Try to determine the angular spread of the transmitted beam and the
range of angles over which the receiver is sensitive. For this purpose define the angular range or
spread as the range of angles left and/or right of center over which the measured signal drops to
10% of the maximum signal. Try to observe interactions of the microwaves with parts of your
body. Record all your observations on the laboratory report form.
2) Line up the transmitter and receiver again and adjust their pointing directions to give the largest
signal possible. Compare the absorption and transmission effects with a metal plate, a wooden
board, and the metal grill with the wires oriented both vertically and horizontally. Insert the
various
objects between the transmitter and receiver with their
Paraffin
faces perpendicular to the line joining the transmitter
and receiver. In each case record the reading on the
Receiver
Transmitter
Paraffin
meter with and without the object. What can you
conclude about the properties of the various
Transmitter
Receiver
substances as far as transmission and absorption of
microwaves?
Receiver
Figure 1a
3) Position the second receiver in the horizontal plane so
Receiver
that it faces at right angles to the line joining the
Figure 1b
transmitter and the first receiver as shown in Fig. 1a.
Make sure the dipole is oriented vertically.
Investigate the reflection effects of the metal plate, wooden board, and metal grid (both
orientations) by placing them at the intersection of the waveguide axes, in the proper orientation
for reflection. In each case, try to adjust the position and orientation of the object to maximize
the signal for the second receiver and record the readings on both meters. What can you
conclude about the properties of the various substances as far as reflection of microwaves?
4) Place one paraffin prism at the intersection of the waveguide axes oriented so that its large face
faces the transmitter at the proper angle for reflection to the receiver at right angles (like the back
prism in Fig. 1b). Adjust its position to give the maximum signal for that receiver and record the
two meter readings. Does the paraffin surface make a very good mirror? Now turn the prism
around as shown in Fig. 1a and adjust its position to give the maximum signal for right angle
reflection. Again record the signals for both receivers. Does the orientation which gives the
maximum signal correspond to what you would expect for total internal reflection of the
microwaves from the diagonal back surface of the paraffin block?
5) Now add the other paraffin block as shown in Fig. 1b and measure the signals at both receivers.
Compare these values to those measured when the paraffin blocks are removed. Finally, with the
paraffin blocks in place, take measurements of the intensity at both the receivers as the second
block is moved away from the first in the direction perpendicular to the diagonal surface. Take
measurements as the separation is increased in steps of four or five mm from zero to about three
cm, being careful keep the first block fixed and the diagonal surfaces as parallel as possible.
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B.
Microwaves as Transverse Electromagnetic Waves
1) The microwaves in this experiment are transverse electromagnetic waves. This means that the
E- and B-fields are at right angles to each other and to the direction the wave travels. The waves
are plane polarized; i.e. the E-field lies in a particular plane (the vertical plane when the
transmitter dipole is vertical). Rotating the transmitter about its axis will rotate the E-field plane
of the generated microwaves. Rotating the receiver about its axis will rotate the detector dipole
and change its sensitivity to microwaves with a given E-field orientation. Remove all objects
between the transmitter and the receiver, placed directly in front of it. Rotate the receiver about
its axis; observe and record how the signal strength changes with orientation. Position the
receiver so the signal is minimum and observe the orientation of the receiver dipole. Is it
horizontal? Orient the receiver so the dipole is exactly horizontal. Rotate the transmitter;
observe and record how the received signal varies with the transmitter orientation. Are your
observations consistent with what would be expected if the microwaves are plane polarized
transverse electromagnetic waves?
2) Direct the transmitter with its dipole horizontal toward a metal plate roughly 70 cm away.
Position the plate so it reflects the microwaves back toward the transmitter. The transmitted and
reflected waves are now travelling in opposite directions in the same region of space. They can
interfere to set up standing waves. Mount the microwave probe horizontally on the stand
provided so the tip of the probe is between the transmitter and the metal plate. Carefully move
the probe back and forth along a line between the transmitter and the plate. You can tape the
meter stick to the table along the direction in which the waves are moving to provide a reference.
You should be able to observe nodes (as signal minima) and antinodes (as signal maxima) in the
standing wave pattern. You might have to move the metal plate slightly to increase the size of
the signals at the antinodes. Why can the exact position of the metal plate make a difference?
(Beware of interactions of your body with the microwaves, which may affect the signal.)
Position the probe at an antinode (signal maximum) and record the position of the probe. Move
the probe along the optical bench and try to observe and count the nodes and antinodes in the
pattern as you pass them. Position the probe at another maximum with 8 to 12 other maxima
between it and the original probe position. Record this final probe position. Estimate the
uncertainty in your measurement of the separation between the two probe positions. Since the
separation between adjacent antinodes in a standing wave pattern is 1/2 wavelength, the
separation between the two probe positions can be used to measure the wavelength of the
microwaves. Note that unless you correctly determine the number of antinodes in the distance
you measure you will not calculate the right wavelength.
3) Re-orient the transmitter so the dipole is vertical. Put the transmitter up on the level of the sink
next to your table. Put the double slit in front of the transmitter. Attach the microwave probe to
the aluminum arm. Record the signal amplitude as a function of angle, taking measurements
every 2.5° from 0° to about 30° relative to the line between the transmitter and the slit board
(note: this line is designated as 90° on the protractor). Then, take measurements every 2.5° from
0° to –15°. Next, cover one of the two slits with a piece of metal, and take measurements every
2.5° from –15° to +15°. (Take care in all these measurements to minimize the reflections of the
microwaves from your body). Finally, record the width of each of the slits, the separation
between their centers, and the distance from the slit board to the center of the microwave probe.
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IV.
Analysis:
Part A
1) What was the angular spread of the microwave beam emitted by the transmitter?
determine this? What is the range of angles over which the receiver is sensitive?
determine this? What evidence did you observe of microwave interactions with
body? Could these have major effects on your measurements in the other
experiment?
How did you
How did you
parts of your
parts of the
2) What can you conclude from your measurements about the absorption, transmission, and
reflection of microwaves by metals and by non-conductors such as wood? Do the reflected
waves satisfy the law of reflection at plane surfaces? How do you explain the difference in
reflection and transmission for the two orientations of the wires when the metal grill is used?
3) Does the plane surface of a paraffin block make a good reflecting surface for the microwaves?
Are your measurements with the single paraffin prism oriented as in Fig. 1a consistent with the
assumption that total internal reflection is taking place inside the paraffin block? The critical
angle of incidence for total internal reflection is:
 c = sin-1 n1 /n2
;
n1 < n2
4) Assume n = 1 for air. If your measurements are consistent with total internal reflection, what
limit do they place on the magnitude of the index of refraction n2 of paraffin for microwaves?
The index of refraction of a medium is n = c/v where c is the speed of the radiation in vacuum
and v is the speed in the medium. What limit do your measurements place on the speed of the
microwaves in paraffin?
5) Make a rough graph of the strength of the signals seen by both the receivers as a function of the
separation between the two paraffin prisms. In a qualitative way, what does this phenomenon
tell you about the electromagnetic field outside the plane diagonal surface of the front paraffin
prism when total internal reflection is occurring? Give reasons for your conclusions.
Part B
1) Summarize your observations of the signal strengths observed for different orientations of the
transmitter and receiver. Make rough plots of signal strength versus orientation angle. In your
own words, tell how the observations support or disagree with the hypothesis that microwaves
are plane polarized transverse electromagnetic waves. What would you expect to observe if the
waves had been longitudinal waves?
2) Calculate the wavelength  of the microwaves from the measured separation between the two
extreme maxima you observed. Remember that the distance between adjacent antinodes in a
standing wave pattern is /2. Calculate also the uncertainty in the wavelength using your
estimated uncertainty in the measured positions of the maxima. Is your measurement of 
consistent with the nominal wavelength of 2.8 cm for the microwave transmitter?
3) The locations of interference maxima in Young’s double-slit experiment are given by:
d sin  = m  m = ( 0, ±1, ±2, …)
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where d is the distance between the slits and  is the wavelength. Plot your data and determine
whether they are consistent with this formula.
The half-width of a single-slit diffraction pattern is given by:
W sin  = 
where W is the width of the slit. Plot your data for the case where one slit was covered,
and determine whether they are consistent with this formula.
(Note: the formula gives the angular offset from the center of the diffraction pattern to
the first minimum on either side. You will not be able to observe the actual minima. [Why?])
Compare this result with the angular spread of the microwave beam determined above, and
explain the difference.
NOTE: Before you leave the lab, all observations and measurements must be completed and
recorded on your lab report form to the satisfaction of your Graduate Assistant.
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