Educational applications of a small Michelson interferometer?

Question

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 $\Delta \lambda\approx \lambda^2/2\Delta d$.

Comments on how these went:

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.

Answer 1

Well I've never played around with a Michelson interferometer (never seen one), but as an undergraduate, I did get to experiment with a Fabry-Perot etalon, that was one cm long. It was supposed to be a one hour lab exercise to measure some spectral lines in the spectrum of a neon discharge tube. The etalon was used in conjunction with a fairly ordinary prism spectrometer that could do coarse spectral dispersion, and the FPE then did quite high dispersion from there. I ended up spending about a month on that one hour project, and determined the wavelengths of about 23 lines in the neon spectrum, to about 1/100 of a wavelength, at orders of around 30,000. The point of this story, is that the neon discharge spectrum is very rich in red, and orange lines, so you might find it an interesting thing to let your students investigate with the Michelson. Now the Michelson, will not give you the same fractional wavelength resolution, that the FP gets, but the sheer number of measurable lines in the neon spectrum, will tweak your students' interest.

PS I ended up having to rewrite the lab manual for the FP experiment, to reflect the fact, that it was not a toy, but a very sophisticated scientific instrument of great precision. It was a relatively simple silvered mirror device with quartz spacers.

Answer 2

What kind of electronics do you have? Any photodiodes? What about a counter? You could use the two to improve your measurement of the Na wavelength by counting fringes electronically. Another variation on your ideas is to put a sealed glass cell into one of the arms and pump it with air to measure the index of refraction of air as a function of pressure. Here are some new ideas.

Idea 1: you could remove one of the rear mirrors and use a laser to readout the motion of a piece of glass. If you play it over a speaker or plug it into a spectrum analyzer you can find the resonant frequencies of a wine glass and use the measured resonant frequencies to destroy it. A slight variation is to use a window pane as the other arm to create a sort of spy device where you can listen to conversations inside of a room.

Idea 2 Suspend the interferometer with three wires to isolate it from ground motion. Remove the rear mirror and attach it to a short post which is rigidly connected to the ground. Now you've got a seismometer! You can use it to read out the local seismic noise at your community college. You can record the data and pass it through a set of band limited rms filters (0.3 Hz - 1 Hz, 1 Hz - 3 Hz, 3 Hz - 10 Hz), you'll find that different types of seismic noise show up in each band. The highest frequencies are anthropogenic sources which will come and go with the work hours. The middle frequencies are known as the microseism and the source will depend on where you are. The lowest frequencies are caused by earthquakes of which there are usually 1 per two weeks that you should be able to see. A typical seismic spectrum is posted below.