Question

Design at least two independent experiments to determine the wavelength of a microwave source. You have a microwave source, microwave detector, a barrier with different regions, and a goniometer to measure angles. (To avoid over-ranging the detector, please use the largest meter multiplier setting that allows you to see what you’re doing. Nevertheless, if you are seeing nothing at any angle, do go to a smaller multiplier.) One of your experiments should involve setting up a standing wave.
One of your experiments should involve Include the following in your report:

a. Design experiments to solve the problem and discuss how you will use the available equipment to make measurements.
b. Describe the mathematical procedures you will use.
c. List the assumptions are you making. Explain how each could affect the outcome.
d. What are the sources of experimental uncertainty? How could you minimize the uncertainties?

Answer 1

Answer:

The Double Slits Experiment and Michelson Interferometer

The questions will be answered for the double slits experiment.

(b) Mathematically, the double slits experiment equation can be given as: d sin 0 = m(Wavelength). d is the separation distance, 0 is the diffraction angle, m = 1,2,3,...

(c) assumptions

The width of the slits is lesser than the microwave's wavelength. This is to set up a standing wave between the microwave source and detector.

m is an positive integer. To obtain a constructive interference of the E-M wave(microwave)

(d) The uncertainties are:

(i)The zero error in the reading of the multiplier will disrupt the value of the wavelength by small percentage. This can be adjusted to obtain more accurate result.

(ii) The angle as obtained by the gionometer can not be measured to highest level of accuracy, as there are some approximations. High sensitive equipment should be used to obtain accurate result

Explanation:

Double Slits Experiment.

The double slits is a pair of 2cm wide slits with a 6cm separation, cut in a metal foil, with the double slits at the centre of turnable with the microwave source and microwave detector through the slits. The shunt on the microammeter is adjusted to

so that a large scale deflection is obtained. The interference pattern may then be explored by moving the receiver arm, whilst keeping the transmitter arm fixed. A graph of intensity (current) versus θ(Measured through the gionometer) should be plotted, and an estimate made of the microwave wavelength by measuring the angular separation of adjacent maxima in the interference pattern and the separation of the two slits.

Michelson Interferometer

Setting up the interferometer, the mirrors are metal sheets and the beamsplitter is a hardboard sheet. The metal sheets should be carefully positioned to be perpendicular to the microwave beam, and the beamsplitter positioned at the centre of the turntable and at 45° to the beam. Any slight change in the path length of either of the beams leaving the beamsplitter changes the interference pattern at the receiver. One of the metal sheets is mounted in a frame which slides along rails. If this sheet is slowly moved, maxima and minima of current will be recorded by the receiver and a plot of “intensity” against distance can be made. The distance between successive maxima (or minima) is one half of the microwave wavelength which can thus be measured.