THE EXPERIMENT

Purpose

To study diffraction and interference patterns produced with microwaves and to use the patterns to determine the wavelength of the microwaves.

Equipment

1. Microwave apparatus (see Experiment 4 for a complete description),
2. Metal plates and magnetic mount bar
3. a meterstick.

A. DETERMINE ₀ FROM SINGLE-SLIT DIFFRACTION PATTERN

Construct a single-slit using two of the metal plates on the magnetic holder bar. Take several trial measurements of the "null" angle to determine a suitable spacing of the slit. The slit must be wide enough that a minimum is produced for < 90; that is, only if /a < 1, or a > ; however, if the slit width is too wide then the spacing between minima will be too small to resolve.

Hints:

• Just as in Exp. 4, there is a basic left-right symmetry available in the apparatus. If you take the average of the angle of a minimum (or maximum) obtained on either side of center, then the systematic errors due to transmitter angle or plate angle will cancel.
• You will have to compensate for "noise" effects which add little peaks and valleys to the expected I vs. functions. When looking for a maximum or minimum, don't be fooled by these artifacts which cause sudden changes over a 1 or 2 angular range.

Once you have found a region of slit widths that give adequate measurements, use the slit width and "null" angle results (at least three slit widths and as many "null" angles as you can find) to determine a value (with uncertainty) for the microwave wavelength ₀.

Choose one slit width to take high resolution data of intensity as a function of angle (~ 2 increments on both sides). Be certain to extend your measurements out past the null angle (20 - 30 points should be sufficient). Plot I vs. , and "fit" your data to the functional form of eqn (2) using an appropriate fitting routine. A function such as the following:

seems to give reasonable results, where A, B, C, and D are the coefficients of the fit. Once again (from the results of your fit) determine a value with uncertainty for the wavelength ₀.

B. DETERMINE ₀ FROM THE DOUBLE-SLIT INTERFERENCE PATTERN

Contruct a double-slit using two wide and one narrow metal plates on the magnetic holder. Be careful to make the slits of equal width. The intensity pattern that you observe is the superposition of the expected two slit interference pattern and a diffraction pattern (as in part A) from each of the two slits. Best results are obtained by choosing the slit widths a < ₀ thereby guaranteeing (see eqn(3) ) that no diffraction minima will occur at values of < 90. You can quickly verify that this condition is met by covering one of the slits and checking that no zero intensities can be found. However, there may still be a substantial reduction in intensity (due to the diffraction pattern) at large angles. Thus, the interference pattern will occur within the central peak of the diffraction pattern, leading to lower intensities at large angles.

Measure the angular positions of as many maxima and minima as possible in the two slit interference pattern. Use these results to determine a value (with uncertainty) for the wavelength ₀. Compare the values of ₀ obtained by the two techniques (diffraction in part A, and interference in part B) to the specified frequency of 10.525 GHz. Which method gives the most precise measurement of ₀ ?