Is the refractive index neglected in the standard Michelson interferometer equation: $\lambda=2d/N$

Question

Hoping someone can help with this. It's a simple question, but I can't seem to find the answer anywhere:

I'm looking at the basic Michelson interferometer experiment, where you measure the wavelength of a laser source by changing the relative path lengths, using the moveable mirror.

The equation I keep coming across for this is $\lambda = \frac{2d}{N} $

But, when I try to figure that out for myself, I get the same equation but with the refractive index in there....

My derivation:

OPL = nL

For constructive interference between the two paths on the interferometer, you need

$\Delta OPL = N* \lambda$ (where N is the number of fringes you 'count')

If I change the location of the moveable mirror by length d, then:

$\Delta OPL = n*2d $ (twice d because it traverses the path twice)

So:

$2dn = N\lambda $

and

$\lambda = \frac{2dn}{N} $

However, the 'standard' equation I see on online lab manuals for this is:

$\lambda = \frac{2d}{N} $

Is the n just neglected because it's close to 1, for air? Or is there something deeper here?

Answer 1

The refractive index of air is effectively equal to 1, so it is often neglected If your interferometer is filled with water or another fluid the refractive index along the beam paths will be that of the fluid (which is different from 1), and your equation is correct.