5. Microwave Optics I
Single Slit Diffraction

Equipment List:
Pasco microwave optics setup.
    transmitter and receiver with power cords
    goniometer
    center stand and long plate
    thin aluminum metal plates

Purpose:
The purpose of this lab is to calculate the wavelength of the microwaves eminating from the provided transmitter using diffraction theory.

Introduction:
About microwaves:

Procedure:
Your slit width should be around seven centimeters. Don't stand too close to the apparatus or else you will reflect the waves back into the receiver and corrupt your data (the is a major source of problems). Set up your equipment as shown in the diagram and your instructor's specifications, and get it aligned and working properly.  The transmitter should be fixed and the receiver will rotate to take relative intensity measurements. The receiver should be placed on that arm of the goniometer so that angles can be read using the small white reference mark. After you have taken your data, you should transform your angles such that the center angle is not 180 degrees but 0 degrees and such that your angles on one side of the "zero mark" will be negative and on the other side, positive.  For the relative intensity settings on the receiver unit, remember to multiply by the appropriate multiplier settings, 30X, 10X etc,. Avoid "pinning" the needle so the receiver will not be harmed.

Conduct a similar experiment to the single slit diffraction lab, but now you will measure the intensity as a function of angle as read from the goniometer. In the picture below, the slit width is not wide enough and their result was not as good as it could have been. The instructor should have caught this mistake.

Data:
Gather more data points closer to and around the first minimum on both sides of the single slit. Gather fewer data points close to the central maximum. Increase the angle and try to get a second order maximum on both sides of the slit. Take twenty to thirty data points.

Analysis:
Using the computers, graph the intensity as a function of the angle. Use a full page graph. Have the x axis incremented in single degrees or perhaps every five degrees. From your graph determine the angle of the various orders for your diffraction minima. You should have at least a first order minimum on each side of the central maximum

Conclusion:
Calculate the wavelength from diffraction theory. One wavelength for the left side angle and another wavelength for the right side angle. Then average those two wavelengths to eliminate certain systematic uncertainties from your experiment (do you know which ones?) For your calculations, use the sine of the angle in degrees; do not use the small angle approximation because the angle is not that small. Compare it to the accepted value. You should get less than five percent discrepancy.