Measure the length of a material with Michelson interferometer

[HotMintea]

Homework Statement

Suppose you know the wavelength of light passing through a Michelson interferometer with high accuracy. Describe how you could use the interferometer to measure the length of a small piece of material.

2. The attempt at a solution

- Sandwich the piece of material behind the movable mirror, and compare the intensity(amplitude) of the light on the detector with the intensity when the mirror is at the initial position. But if I know how to sandwich it without compressing it, that means I already know the length of it. Even if possible, I think this won't tell whether the length is x or x+mλ/2 for integer m, so I must make the wavelength of the light longer than twice the length of the material. I read that the wavelength of far-infrared light can be about 1mm, so the material should be smaller than 0.5 mm.(http://en.wikipedia.org/wiki/Infrared#CIE_division_scheme) (Is there a type of light with longer wavelength than infrared?)

- Put the material in 1 of the 2 paths of light, and compare the light intensity on the detector with that when there is no material. But I realized I don't know any way of holding the material without restricting the path of light. Plus interference is irrelevant in this case.

Please correct my mistakes and provide some hints!

 

[ideasrule]

(http://en.wikipedia.org/wiki/Infrared#CIE_division_scheme) (Is there a type of light with longer wavelength than infrared?)

Microwaves and radio waves are both EM radiation with much longer wavelengths, but they're not practical to work with using a conventional Michelson interferometer.

- Put the material in 1 of the 2 paths of light, and compare the light intensity on the detector with that when there is no material. But I realized I don't know any way of holding the material without restricting the path of light. Plus interference is irrelevant in this case.

Actually, interference isn't irrelevant. Assuming you know the material's index of refraction, how does the interference pattern change when you put the material in 1 path but not another? Remember that the pattern is initially circular, like this: http://www.phys.unsw.edu.au/PHYS1241/links_light2/michelsn.htm

 

[HotMintea]

Microwaves and radio waves are both EM radiation with much longer wavelengths, but they're not practical to work with using a conventional Michelson interferometer.

Could you explain why microwaves and radio waves are not practical for a conventional Michelson interferometer? (Or could you perhaps provide some keywords, so that I can look them up?)

Actually, interference isn't irrelevant. Assuming you know the material's index of refraction, how does the interference pattern change when you put the material in 1 path but not another? Remember that the pattern is initially circular, like this: http://www.phys.unsw.edu.au/PHYS1241/links_light2/michelsn.htm

Thanks for pointing it out. I was imagining light cannot pass through the material. Either way, my 2nd prospect doesn't seem to work unless there is a way to hold the piece of material without getting in the way of light.

Assuming both of my prospects don't work, I would like some hints at this point.