The purpose of this lab experiment is study interference and diffraction of light waves using the microwave apparatus.

Lloyd's Mirror Experiment

In the previous experiment, you observed how a single electromagnetic wave can be diffracted into two waves, causing constructive and destructive interference to occur. The same result may be achieved using Lloyd's Mirror, providing a convenient method for measuring the wavelength of the radiation.

Figure 1. Lloyd's Mirror.

A diagram of Lloyd's Mirror is found in Figure 1. Here electromagnetic radiation from one source at point A is detected by a receiver at point C. If radiation from A is reflected off a mirror at point B, the reflected wave will also be detected by the receiver. Due to the reflection from the mirror, the reflected wave will be 180° out of phase with respect to the incident wave. When the two waves meet at the receiver, constructive and destructive interference can occur. A maximum signal will be detected when the two waves reach the detector in phase.

From Figure 1, the optical path length, , of the reflected wave is defined as . The optical path length of the un-reflected wave is

Figure 2. Lloyd's Mirror with two optical path lengths displayed for the reflected wave.

For constructive interference to occur, the optical path lengths for the reflected wave and the un-reflected wave must be some multiple of the wavelength, . The position of the mirror, , may be varied to obtain a series of maxima and minima intensities at the receiver as shown in Figure 2. Therefore, for particular values of the condition for constructive interference is

(1)

where . The quantity is the fringe number. Fringes can be seen as the dark and light bands of Figure 3.

Figure 3. A fringe pattern for the single-slit Fraunhofer diffraction pattern. (From Serway and Beichner, 5th Edition, page 1218.)

Double-slit Experiment

The background for the double-slit experiment will be given to you by your TA.

1. Setup the Lloyd's Mirror experiment and reposition the mirror to obtain as many fringes as possible. For each subsequent fringe number, determine a value for . Average these values to find a mean value for . Determine the standard deviation for the measurements.

2. Use your data from Objective 1 and make a plot to determine .

3. Setup a double-slit apparatus using the provided materials. Take readings of intensity of the diffracted wave through a large angle using small increments, being sure to also obtain the angles of maximum intensities. Make a plot of intensity versus angle. Use one of your previous calculations of and determine the slit separation, . Perform a propagation of uncertainty for this objective.

(Figure 4.) Lloyd's mirror setup. (Figure 5.) Double slit diffraction setup.

[Click on images to enlarge.] 4 5

1. Caution!!! Although the microwave power levels from this apparatus are not harmful, microwaves do cause water molecules to resonate, therefore never point the klystron (transmitter) at your body, especially toward your eyes.

2. Allow the klystron about 2 minutes to warm up before beginning your experiment.

3. Objective 1 requires very careful experimentation techniques. Keep the equipment properly aligned.

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Each lab group should download the Lab Report Template and fill in the relevant information as you perform the experiment. Each person in the group should print-out the Questions section and answer them individually. Since each lab group will turn in an electronic copy of the lab report, be sure to rename the lab report template file. The naming convention is as follows:

For example the group at lab table #5 working on the Ideal Gas Law experiment would rename their template file as "5 Gas Law.doc".

Each student should download the questions. Each person in the group should print out the questions and answer them individually. Discussing the questions as a group is acceptable, but each student is responsible for turning in answers that represent their own work, not the work of others.

These Nudge Questions are to be answered by your group and checked by your TA as you do the lab. They should be answered in your lab notebook.

Objective 1 Nudges

1. Are the initial locations of the transmitter and receiver important to consider?
2. From what points are the graduations on the goinometer referenced?
3. How did you calculate the optical path length for the reflected waves?
4. How many fringes were you able to detect?
5. Why does the intensity of the fringes decrease as increases?
6. How many calculations of were you able to make?
7. What is the standard deviation of the measurements?
8. What do you expect the value of to be?

1. What parameters will you plot to determine ?
2. How did the Objective 2 and 3 values of compare?

1. Are the initial locations of the transmitter and receiver important to consider?
2. What is the initial angle of the receiver?
3. Should the transmitter be moved during the experiment?
4. How many intensity readings did you make? Why?
5. How many fringes did you detect?
6. Why does the intensity of the fringes decrease with angle?
7. How will you calculate the slit separation?
8. How will you measure the slit separation?
9. How does the calculation and measurement of compare?

As of now, there are no CUPOL experiments associated with this experiment.