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

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?

• Yes............ Mar 26 '19 at 21:34