# Educational applications of a small Michelson interferometer?

The community college where I teach has some nice old Michelson interferometers. There appear to be a bunch of versions of these that used to be sold (may still be sold?) which were all probably knock-offs of some manufacturer's original model. Ours are Cenco 71990-549, and are identical to the one in the photo here (but without the stepping motor). Here and here are manuals for a couple of other similar ones. (We no longer have the manuals for ours.) The arms are about 20 cm, the movable mirror can travel about 25 mm, and it has a micrometer that is accurate to about 2 um.

What is a good educational application for these sweet old instruments?

Here are the things I've tried, both by myself and using students as guinea pigs:

1. Crank the micrometer while counting fringes with a Na discharge tube. Determine the wavelength.

2. Like 1, but with laser light, projecting the fringes rather than squinting into the instrument.

3. Equalize the arms by finding the condition where fringes are visible with white light. Insert a sample of glass with an unknown index of refraction, and reacquire the condition of equal optical path length. Determine the unknown index of refraction.

4. The Na line is actually a close doublet, so as you move the micrometer you go back and forth from a condition of high-contrast fringes (the bull's eye patterns for the two wavelengths agree) to a condition of little or no contrast (the patterns disagree and counteract each other). If $\Delta d$ is the distance traveled between two successive positions of maximum contrast, then the splitting of the doublet is $\Delta \lambda\approx \lambda^2/2\Delta d$.

1. Incredibly tedious, and nearly impossible to do with high precision because you pass through the conditions of low contrast described in #4. The same result could be obtained with much higher precision in five minutes with a diffraction grating.

2. Not as bad as #1, but still doesn't use the instrument for an application to which it's uniquely well suited.

3. This was very cool. It was amazing how accurately the equal-length condition could be detected using this technique (to within 1 um). However, it doesn't seem to be a high-precision way to determine an unknown index of refraction, because you have to use a thin sample like a microscope slide, and your precision ends up limited by the determination of the thickness of the slide using Vernier calipers (e.g., 1.8 mm, so only 2 sig figs).

4. This is sublimely tricky, but I doubt that most students understand it. Measuring the spacing of a close doublet, while impressive to a spectroscopist, is of little intrinsic interest to a student in a freshman survey course.

Other than the Michelson-Morley experiment (which obviously can't be done in a 3-hour student lab with a tabletop instrument), the classic historical application seems to have been the determination of the meter in terms of atomic standards. (See Hardy and Perrin, p. 584.) This doesn't seem practical for us.

I've seen references to gas cells for use with this setup, presumably using the technique of #3. A back-of-the-envelope calculation seems to suggest that you would get a low-precision measurement, so I don't really see the point.

Is it possible to use a technique sort of like #3 to determine the ratio of two wavelengths from the same source with high precision? This would have some intrinsic interest for hydrogen, whose wavelengths are in the ratios of small integers.

• One simple demo that I've used is to show the sensitivity by pressing lightly on the bed. On the one I used, it was easy to shift fringes by light pressure on the cast-iron base... – DJohnM Oct 17 '13 at 3:13