Deriving the Michelson Interferometer Equation: d_m = (m[lambda])/2

[NovaKing]

does anyone know how to derive this equation regarding the Michelson interferometer:

d_m = (m[lambda])/2

where d_m is the physical distance of a micrometer division, m is the number of fringes that crosses a screen given some d_m and lambda is the wavelength of the laser used to create the interference pattern.

I understand that the path difference divided by the wavelength is responsible for the number of fringes that pass by a certain mark, but I don't understand where the 2 comes from. Can someone help me please?

 

[NovaKing]

oh hehe never mind.


as it turns out because the path difference divided by the wavelength is number of fringes that pass I can set up a diagram to evaluate the problem.

Quite simply, the change in distance for the interferometer which has an arm that changes length is just 2L - 2(L-d_m) which gets 2d_m as the change in distance. Thus:

2d_m = m[lambda]

or

d_m = (m[lambda])/2


how silly of me