ali8 wrote:http://grephysics.net/ans/9277/96

Hi,

So basically all the resources on the net use this formula as if it's "too well known" to be explained.

Where m is the number of fringes observed, and L is the length of the gas-cell in the Michelson Interferometer.

I just want to know where I can find a derivation for this formula. I know in PGRE one won't derive anything

but I want to learn, not just to pass PGRE.

In the interferometer, the light passes through a medium with a refractive index differing from the environment by

. Since the medium is of length L, and it passes through twice, the light is slowed by some amount

(the phase shift). Since a fringe occurs when the wavelengths match, you get maximum constructive interference (a fringe) any time the phase shift is an integer multiple of the wavelength. Thus,

equals

, which after dividing by 2L gives the above formula.