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hm29168

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## Homework Statement

Giancoli Ed. 6, Ch. 24, #52

One of the beams of an interferometer passes through a small glass container containing a cavity 1.3 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610nm. Calculate the index of refraction of the gas, assuming that the interferometer is in a vacuum.

## Homework Equations

For destructive interference:

Distance traveled = (m+0.5) * wavelength

where m is in the set 1, 2, 3...

## The Attempt at a Solution

http://en.wikipedia.org/wiki/File:Interferometer.svg is a picture of an interferometer. The gas chamber is placed between the silvered mirror and the mirror on the right and the reflections are in line with each other instead of slightly at an angle in this case.

Let d be the difference in distance between the beam going through the gas and what the beam would be not going through the gas. Since the light passes twice through the gas chamber, the total difference in distance will be 2d. Plugging into our equation, we get

[tex]2d=(236+\frac{1}{2})\cdot(610\cdot10^{-9})[/tex]

[tex]d=7.21\cdot10^{-5}[/tex]

Armed with the distance, I should be able to find the index of refraction of the gas using Snell's law. However, I am not sure if I am calculating the extra distance traveled correctly. I also don't know how to find the index of refraction if the beam of light is in line with the normal of the medium.

Thanks for all of your help!