# Measure the length of a material with Michelson interferometer

• HotMintea
In summary, using a Michelson interferometer, one can measure the length of a small piece of material by sandwiching it between the movable mirror and the detector and comparing the intensity of light with and without the material. However, this method only works if the material is not compressed and if the wavelength of light is longer than the length of the material. Alternatively, the material can be placed in one of the light paths and the interference pattern observed, but this method requires a way to hold the material without obstructing the light. Microwaves and radio waves have longer wavelengths than infrared, but are not practical for use with a conventional Michelson interferometer. Knowing the material's index of refraction can help determine the changes in the interference pattern
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!

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HotMintea said:
(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

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ideasrule said:
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?)

ideasrule said:
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.

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## 1. How does a Michelson interferometer measure the length of a material?

A Michelson interferometer uses the principle of interference to measure the length of a material. It sends a beam of light through the material and splits it into two beams. One beam is reflected off a fixed mirror, while the other is reflected off a movable mirror. When these beams recombine, they create an interference pattern that can be used to calculate the length of the material.

## 2. What is the accuracy of a Michelson interferometer when measuring length?

The accuracy of a Michelson interferometer depends on various factors such as the quality of the optics, stability of the instrument, and the wavelength of light used. Typically, it has an accuracy of 0.01 micrometers (µm) for measuring length.

## 3. Can a Michelson interferometer be used to measure the length of any material?

Yes, a Michelson interferometer can be used to measure the length of any material that is transparent to the wavelength of light being used. However, the material must also be flat and have a smooth surface to ensure accurate measurements.

## 4. What are the advantages of using a Michelson interferometer for length measurements?

One of the main advantages of using a Michelson interferometer is its high accuracy. It is also a non-contact measurement technique, which means that it does not physically touch the material being measured, making it ideal for delicate or sensitive materials. Additionally, it can measure both small and large lengths with equal precision.

## 5. Are there any limitations to using a Michelson interferometer for length measurements?

One limitation of using a Michelson interferometer is that it requires a stable and controlled environment to ensure accurate measurements. Any vibrations or temperature changes can affect the measurements. It also has a limited range of measurement, typically up to a few millimeters. Additionally, the material being measured must be transparent and have a smooth surface for accurate results.

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