Microwave Diffraction and Interference
Department of Physics
Ryerson University
rev.2014
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Introduction
The object of this experiment is to observe interference and diffraction of microwave radiation, and to use the observations to measure the wavelength of the microwaves. The
absorption of microwaves by materials will also be observed.
Microwaves are electromagnetic waves which have wavelengths in the λ ∼ 1mm − 30cm
range, with corresponding frequencies ν ∼ 109 − 3x101 1Hz. They can be generated with
a vacuum device known as a klystron, a solid state device called a Gunn oscillator, and
by a magnetron, used in domestic ovens and high power transmitters. Here, we will use
a Gunn oscillator to explore the wave properties of microwaves through double and single
slit experiments, as well as their absorption by materials.
1.1
Equipment
• Gunn Diode Microwave Transmitter, ν = 10.525GHz, λ = 2.85cm
• Microwave Receiver
• Goniometer
• 2 x metal reflector, 1 narrow slit spacer
• Magnetic component holder
• Slit Extender Arm
• paper towel
1.2
Precautions
The intensity of the microwave beam emerging from the microwave horn is within the
limits of what is considered safe. However, to be on the safe side, avoid any unnecessary
exposure of any part of your body to the radiation. It is especially advisable not to expose
your eyes to the source of the microwaves at close range.
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2
Double Slit Interference
The objective of this part of the experiment is to observe the interference of microwaves
and to use these observations to find their wavelength.
Microwaves spreading out from a single source can be divided by openings in a metal
screen. The beams coming from the two openings are coherent, will spread out (diffract)
and interfere with each other. For some locations the interference will be constructive and
for others it will be destructive with gradual changes from constructive to destructive in
between.
The type of interference is seen to depend on the angle, θ, at which the waves are
observed. The angle is measured with respect to the centre line drawn through the midpoint
between the two openings in the screen and perpedicular to the screen. The values of the
angles for which constructive interference should be observed are given by the following
equation:
d sin θ = mλ
(1)
where d is the centre to centre space between the screen openings, λ is the wavelength
of the waves, and m is a positive integer (m = 0, 1, 2, ...).
2.1
Procedure
1. Obtain the goniometer with microwave transmitter and receiver mounted at either
end. The transmitter should be mounted on the fixed arm of the goniometer, at least
30 cm from the centre. The reciever should be mounted on the movable arm of the
goniometer, as far from the centre as possible. The movable arm should be at 180◦ .
2. Set the small metal sheet at the centre of the magnetic mount, and one of each of
the other larger metal plates on each side. Adjust the spacing such that the spacing
is roughly 1.5 cm, with the same slit spacing on either side. Ensure the slits are
oriented perpendicular to the lab bench. Ensure the magnetic component holder is
aligned perpendicular to the microwaves.
3. Plug in your transmitter and turn on your reciever to the 30x range. Your reciever
has 4 ranges. If you read a current in the 30x range, you need to multiply the reading
by 30x in order to get the actual value. There is a variable sensitivity knob. If you
need to adjust the variable sensitivity knob, do not adjust it for the remainder of the
measurement. Adjust the multiplier of the reciever until it reads ∼80% of full scale.
If 1x does not give sufficient signal, you can use the variable sensitivity to acheive a
sufficient signal.
4. Quickly survey the range over which you will take data (120◦ to 240◦ to verify your
diffraction pattern looks approximately as expected. Request assistance from your
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TA if you are not seeing the approximate expected pattern of maxima and minima
before proceeding.
5. Record receiver meter readings as a function of angle up to 60◦ on both sides of the
centre, at 2◦ intervals.
6. Measure the centre to centre separation d of the two openings in the screen.
2.2
Analysis
Plot the intensity data as a function of angle θ with a smooth curve between points.
Determine the angle separating each side maximum from the centre maximum and average.
Estimate the uncertainty in this angle.
Use Equation 1 and the average location of the maxima to get an estimate of the
microwave wavelength and the uncertainty of this value. Compare and comment on the
specified value for the Gunn Transmitter. Does your range of uncertainty include the
manufacturer’s value for wavelength?
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Single Slit Diffraction
The image of a point source passing through a small opening can be characterized as a
fuzzy central image surrounded by concentric fuzzy bands of light. The angular separation,
θ, of the first minima (dark space) is inversely related to the size of the opening, a, and
proportional to the wavelength λ:
λ
(2)
a
where k is a constant of proportionality which depends slightly on the shape of the
opening. For a rectangular opening, k = 1, but for a circular opening, k = 1.22. The
objective is to observe the single slit diffraction pattern and obtain a rough estimate of the
wavelength of the microwave source.
sin θ = k
3.1
Procedure
1. Using the two large metal screens, create a 1.5 cm opening, mounted in the middle of
the magnetic component holder. The reciever should again be as far from the screen
as possible. Adjust the sensitivity such that the central maxima gives roughly 80%
of full scale.
2. Record receiver meter readings as a function of angle up to 60◦ on both sides of the
centre, at 2◦ intervals.
3. Repeat steps 1 and 2, using a slit width of 6 cm.
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3.2
Analysis
Plot relative power versus angle for both the 1.5 cm slit and 6 cm slit on the same graph
as the double slit. Comment on any similarities between the two patterns. Estimate the
angular separation of the minima, if they are present, on either side of the central maximum
for each pattern, including the uncertainty in these minima.
Note that the larger opening results in a narrower pattern of received power. If possible,
estimate the wavelength of the microwaves using Equation 2 for single slit diffraction and
the uncertainty. Compare to the stated wavelength for the Gunn diode. Does your range
of uncertainty include the manufacturer’s value for wavelength?
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Absorption of Microwaves by Wet and Dry Materials
The object of this part of the experiment is to observe the ability of water to absorb
microwaves.
4.1
Procedure
1. Adjust the reciever to 180◦ and the recieved power to 80% of full scale. Remove the
magnetic mount.
2. Record the meter reading with no material between the transmitter and receiver.
3. Crumple a paper towel and place in the receiver horn. Record the meter reading.
4. Remove the paper towel from the horn and wet it. The towel should be damp but not
dripping. Place the damp towel in the receiver and record the new meter reading.
5. Try other types of materials as available: plastics, cloth, etc.
4.2
Analysis
Compare the reading of the wet and dry paper towels, and any other types of material you
may have used. What can you conclude from these observations?
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References
[1] Instruction Manual and Experiment Guide for the PASCO Scientific Model WA-9314B,
PASCO Scientific, 1991.
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