Michelson's Interferometer Problem

[VitaX]

Homework Statement

[PLAIN]http://img828.imageshack.us/img828/7386/physicsch3581.png

Homework Equations

Not sure

The Attempt at a Solution

the indicies of refracton are inversly related to the speeds, that is n=c/v . You find the time to go distance L in one arm t=L/v with air and the other with vacuum t=(L+dL)/c dL=(fringes)*wavelength

My substitute teacher gave us that as a hint, but I really don't see how that relates to the problem, or rather I don't see any of those equations in the section over the interferometer.

I see N_m = 2L*n/λ
N_a = 2L/λ
N_m - N_a = 2L*n/λ - 2L/λ

I really don't know where to begin on this problem, we never did any examples of it in class.

 

[Fewmet]

I recommend that you focus on the logic of the Michelson interferometer. You split a light beam and then recombine it: why does interference occur?

If you have that down, think though the effects of changing the speed of the one beam by putting it through a vacuum rather than air.

You might also look at https://www.physicsforums.com/showthread.php?t=358946", which is about a very similar problem.

 

[VitaX]

Ended up using Nm - Na = 2L*n/λ - 2L/λ and solved for n. Ended up with the books value of 1.0003.