Microwave Optics

Chabot College Physical Science

Scott Hildreth

Experiment Goals: Demonstrate the wave nature of light, including reflection, refraction, polarization, interference, and diffraction, using microwaves. Along the way, experimentally test the inverse square law, that light intensity decreases with the square of the distance away. And test that the angle of incidence of a beam is the same as the angle of reflection, as well as Snell’s Law, that the angle of refraction depends upon the index of refraction of materials. We’ll also explore the physics of Young’s double-slit experiment as well as interferometers.

Lab Safety Note! Although the microwaves in this experiment are not inherently dangerous, they can cause water to evaporate, and consequently they should never be aimed at the eyes. They are generated by a klystron tube, which also will heat up during the experiment. Be careful not to touch it.

A: Calibrate the system, explore the intensity at different distances, and determine the wave shape.

Arrange the transmitter and receiver in a straight line on the “goniometer” (a device used to measure angles). Be sure the horn antenna and receiver are in the same orientation (the ‘polarity’), either horizontal or vertical. Plug in the transmitter and turn the intensity switch on; it will take 1-2 minutes for the transmitter to warm up and produce consistent intensity waves.
Adjust the distance between the emitter and detector diodes (located just at the small end of the horn antennae) so that they are about 40 cm apart. Adjust the intensity dial so that the meter reads 100 on the receiver. Now vary the distance between the transmitter and receiver (sliding the receiver along the track) and record – including uncertainties – the following data:

Distance R (cm)	Uncertainty	Meter Reading M	Uncertainty	M x R (cm)	Uncertainty	M x R² (cm²)	Uncertainty
40
50
60
70
80
90
100

Finally, undo the four plastic screws holding the receiver’s antenna horn, and rotate it slowly (from horizontal to vertical) while you watch the meter. Make a sketch of the orientations of each device (transmitter and receiver) and at what angles the intensity is maximum and minimum. When completed, please put the horn back on the receiver in its initial orientation.

Additional questions to answer for part A:

Light of any wavelength is a combination of oscillating Electric and Magnetic Fields. The strength of the Electric field of an electromagnetic wave is inversely proportional to the distance from the source, in other words, E = C1/R, where “C1” is a constant.

If you rearrange this equation, C1 = ER, so the product of the E field strength time distance should be constant. From the results in step 2, is the meter reading E field strength? Look at the values in the MxR column. Are they the same? How does your uncertainty affect this conclusion?

The intensity of the wave – which is the power of the wave over the area it falls on, should decrease proportional to source distance squared. In other words, I = C2/R², where C2 is a different constant. From the results in step 2, is the meter reading overall wave Intensity? Look at the values in the MxR² column. How does your uncertainty affect this conclusion?
From observations in step 3, can you estimate the direction of the wave’s electric field? This direction determines the “polarization” of the wave.

B. Exploring Reflection

Set up the system with a flat metal reflecting plate (a microwave “mirror”) at the central point, and vary the incoming “incident” light from the transmitter between 10 to 80 degrees. Rotating the receiver on the goniometer, measure and record the angle of reflection - and your uncertainty – where the receiver intensity is maximized.

Incident Angleº	Max Intensity Reflected Angle (+/- ?)	Incident Angleº	Max Intensity Reflected Angle (+/- ?)
10		50
20		60
30		70
40		80

Additional questions to answer for part B:

Does the angle of incidence appear to be the same as the angle of reflection? How certain are you given the uncertainties in measurement in this lab?
Note in your data for reflection (Table B1) where the incident and maximum intensity reflected angles do not seem to be the same. What might be causing this result? What could you do to minimize the effect?
Ideally this experiment would be performed using the incoming light as a “plane” wave. Is it? (Consider your result from part A.) How would the departure from a plane wave affect this particular experiment?

C. Exploring Refraction

Set up the system with the arms of the goniometer initially 180 degrees apart, parallel to the long side of the lab tables. Place the empty semi-circular Styrofoam (acting as a microwave “lens”) at the central point, so that the incident light falls on the CURVED side of the container. The flat side of the container should be exactly at the rotation axis. (Figure C1)

In one more step, you’ll fill the empty container with polystyrene beads, and determine their index of refraction for microwave radiation. But good experimental technique involves ensuring that the container alone doesn’t interfere with your results. Design a short experiment to determine whether the Styrofoam container alone refracts the microwaves. Describe what you did, and your results.
Now fill the container with polystyrene beads. Vary the incoming “incident” light from the transmitter between and 70 degrees. Being careful to ensure that you are measuring the proper angles (see Figure C2!), rotate both the transmitter and the receiver on the goniometer, and then measure and record the angles of incidence and refraction - and your uncertainty – where the receiver intensity is maximized.

Refraction data: Polystyrene beads

Incident Angleº (+/- ?)	Max Intensity Refracted Angle (+/- ?)	Incident Angleº (+/- ?)	Max Intensity Refracted Angle (+/- ?)
0		40
10		50
20		60
30		70

Additional questions to answer for part C:

From your data, using Snell’s law, n₁sin (q₁) = n₂ sin (q₂), find (n2), the average value of the index of refraction for the polystyrene beads for this wavelength of microwaves. Here, n₁ will be 1 (meaning that the speed of light in air is almost as big as it is in a vacuum).

so: n₂ = sin (q₁) / sin (q₂)
What is the uncertainty in your measurement of n₂?
Do you believe your results will change if, rather than using small beads, you used a solid block of polystyrene? Why?

Optional explorations: Use paraffin rather than polystyrene beads and determine its index of refraction.

D. Exploring Interferometry

Set up the system with two sets of extension arms, a partial metal mirror at the center, two solid metal mirrors, and a moveable threaded clamp as shown:

Before connecting the moveable mirror to the threaded clamp, move it along the track towards the transmitter and verify that the receiver intensity oscillates. Then position the moveable mirror at a location of maximum intensity, attach the threaded clamp, and tighten the clamp to the track. Record that position along the moveable mirror arm of the goniometer.
SLOWLY advance the moveable mirror by rotating the knob on the threaded clamp, and note where the minimum intensity occurs. Record that distance. Continue to advance the mirror until you reach another maximum, and again record the distance. From your data, determine the actual wavelength of the microwaves, and its experimental uncertainty based on your measurements.
What is the major limiting factor in your precision with this trial? Design an experiment that will improve the precision of your experimental result. Carry it out, and compare your results.

E. Exploring Two-Slit Interference

Set up the system with a double-slit reflector at the central point on the goniometer: Measure the slit size, and slit separation (d) - the distance between the center of the slits.

Rotate the receiver on the goniometer arm slowly to verify that you see maxima and minima as the angle varies. Measure and record where the maxima are apparently located in the receiver – but don’t forget to include the uncertainty in your angle. Also calculate d sin q for each angle.

Angleº (+/- ?)	Maxima Meter reading	d sin q

Do you see any pattern in the values of d sin q as you move to larger and larger angles? Compare those values to the wavelength of microwaves found in your interferometer step 19.

Microwave Optics

Chabot College Physical Science

Scott Hildreth

F. Exploring Single-Slit Diffraction

Set up the system with a single-slit reflector at the central point on the goniometer: Measure the slit size (a).

Rotate the receiver on the goniometer arm slowly to explore whether you see maxima and minima and record the angles where the minima are apparently located in the receiver. Don’t forget your uncertainty in those measurements.

Angleº (+/- ?)	Minima Meter reading	a sin q

Calculate a sin q for each angle, and examine your calculated results. Do you see any pattern here related to the wavelength of the light? Discuss how your measurement uncertainties affected your results. Compare this experiment to the two-slit interference pattern in terms of your results, and your uncertainties.

Microwave Optics

Chabot College Physical Science

Scott Hildreth

G: Exploring Polarization

Insert one of the multi-slit barriers between the transmitter and receiver, and then rotate it 90 degrees. What happens to the received radiation as you rotate the barrier?

Put the first barrier vertically, and a second multi-slit barrier between the receiver and transmitter, oriented at 90 degrees to the first. What happens to the received radiation?

Put a third multi-slit barrier between the first and second barriers (still oriented at 90 degrees to each other.) Align the third barrier to be 45 degrees between the first two. What happens to the received intensity?

second barrier horizontal