Michelson interferometer

Set up a Michelson interferometer according to the sketch in Figure 4.1. The mirrors are aluminum sheets, and the beamsplitter is a piece of coarse wire screening. Take some care to make certain that the mirrors are perpendicular to one another, and that the beam from the source illuminates Mirror A on a line that is also perpendicular to its surface. You may need to move things just a little, but with minor adjustments you should find a strong signal with the detector at the position shown in the figure.

Carefully set a ruler next to Mirror A. Slowly move the mirror away from the beamsplitter and watch the strength of the signal. You should see a very clear drop in signal as you do this. For some positions of the mirror the signal will be nearly zero, and for others it will be quite strong. These are fringes caused by interference for the two possible paths through the interferometer. If $y$ is the position of Mirror A, then a maximum will occur whenever

$$m \lambda = 2 (y + y_0)$$

where $y_0$ is an unknown constant, and $m$ is an integer order of interference.

Use this relationship to find the wavelength $\lambda$ of the microwaves. Start with Mirror A close to the beamsplitter. Move it slowly back from the beamsplitter, and at each position where the signal drops to a minimum record the position of the mirror. Since $y_0$ is unknown, the initial starting point is immaterial, as is the point on the mirror support from which you take the position measurement. Be careful not to miss any minima, however. You should be able to find $10$ or more in this way. Enter the data in a file with $m$ and the ``x'' entry and $y$ as the ``y'' entry. Use xmgr to display the results. If you accidentally missed a minimum you will notice it now as a extra step in the plot. If that happens, you should locate the missing minimum and include its position before continuing. Fit the data with a straight line. The line will be the solution

$$y = m \lambda / 2 - y_0$$

The slope of this line is

$$dy/dm = \lambda / 2$$

What is the wavelength of the microwave emission from this klystron? Use $\lambda \nu = c$ to evaluate the frequency of the microwaves.

Include screen dumps of the xmgr files with your lab report. Before you disturb the setup used for this measurement, you should complete the last part of the experiment described in the next section.

Figure 4.1: With microwaves the Michelson interferometer is simple to set up, and not critically dependent on alignment. A parallel beam with a few milliwatts of microwave emission from the klystron is split at the Beamsplitter. Half of the beam goes to the right and half to back. After reflection, the two beams return to the Receiver where they interfere and are detected.