# Fabry-Perot interferometer

1. Jul 12, 2011

### HotMintea

1. The problem statement, all variables and given/known data

A Fabry-Perot interferometer has spacing d = 2 cm between the glass plates, causing the direct and doubly reflected beams to interfere. As air is pumped out of the gap between the plates, the beams go through 23 cycles of constructive-destructive-constructive interference. If the wavelength of the light in the interfering beams is 5 × 10^−7 m, determine the index of refraction of the air initially in the interferometer.

2. Relevant equations

(I think) If constructive interference is occurring, 2d = mλ/n, for wave length λ, refractive index n and some integer m.

3. The attempt at a solution

I cannot figure out how to incorporate the following part in the equation: "As air is pumped out of the gap between the plates, the beams go through 23 cycles of constructive-destructive-constructive interference."

2. Jul 12, 2011

### SammyS

Staff Emeritus
It means that m changes by 23.

Can you say which it did? Did m increase? or Did m decrease ??

Also, assuming that virtually all of the air was pumped out, what is the index of refraction for a vacuum ?

3. Jul 12, 2011

### HotMintea

Since wavelength gets longer as the air gets thinner, I think the number of wavelengths in the distance 2d will decrease as the air gets pumped out.

The index of refraction in vacuum is defined to be 1.

I have: m λ/n = (m - 23) λ/1 = 2d. The left side says integer m times the contracted wavelength λ/n. The middle says (m - 23) times full length λ/1. The right side is twice the gap.

Solving the left and middle, I get m = (2d + 23λ)/λ. Substitute it for m in the left and solving the left and right, I get n = 1 + 23λ/2d.

Last edited: Jul 12, 2011
4. Jul 12, 2011

### SammyS

Staff Emeritus
What do you get for a numerical answer for n-1? (Just out of curiosity .)

5. Jul 13, 2011

### HotMintea

6. Jul 13, 2011

### SammyS

Staff Emeritus
Excellent !