A review of the broader principles of interferometry can be found at this optics course website (caveat emptor):
http://electron9.phys.utk.edu/optics421/modules/m5/Interferometers.htm
A Touch of Theory:
Constructive interference between the two arms of the interferometer occurs when:
2λnl=Δ
Where Δl is the distance that one of the mirrors moves relative to the other mirror. In this experiment, mirror #2 is moved. n is an integer (not zero) and λ is the wavelength of the light source.
The previous equation is arrived at with the following argument: When the mirror mounted on the translation stage is moved (λ/2, then the light in that arm of the interferometer moves one whole wavelength, and the interference pattern changes from a maximum to a minimum and then back to a maximum.
What this means is that, for instance, if you are looking at the bright center of a circular interference pattern, as the translation stage is slowly moved (λ/2, the central bright region should turn to a dark minimum and then back to a bright maximum. This is what is termed the movement of one whole fringe, with n=1, or better yet, Δn=1. If, as is done later in the lab, the pattern’s central region is moved (with the movement of one of the mirrors) from bright to dark, and then back to bright, say, fifty times, then Δn =50.
The only other equation needed for this lab has to do with the experimental setup of the interferometer. Since the mirror is not moved directly with the micrometer but through a lever system, the relationship between the distance the mirror moves to the distance the micrometer moves is proportional theoretically to:
mklΔ=Δ