Calculating Maxima in 1-D Wave Interference with a Half-Silvered Mirror

[XJellieBX]

Homework Statement

Monochromatic light of wavelength \lambda = 400 nm enters at A. It impinges on a ‘half-silvered mirror’ B, which directs some of the light to mirror C, while passing the rest to mirror D. Some of the reflected light from mirror C passes back through the half-silvered mirror, where it combines with reflected light from D, arriving at the detector. Mirror C is attached to a micrometer, so that it can be moved to change the path length B − C − B.
If mirror C is moved through 10 microns (1 micron is 10−6 m), how many maxima will be
observed at the detector? Assume that the intensity at D is intially a minimum.

Homework Equations

D(x,t)=asin(kx-wt+\phi_{0}

The Attempt at a Solution

I'm actually not sure how to approach this to begin with, so any advice is appreciated. I've also attached a copy of the diagram. I'm thinking this might have something to do with the path length being x₁ and x₂

 

[tiny-tim]

Hi XJellieBX!

If mirror C is moved through 10⁻⁶ m, how much longer does that make the path?

So how many wavelengths is that? And how many maxima will go past?

 

[XJellieBX]

So if I find how many wavelengths that is, which i did find, i can figure out the number of maxima. I'm just not too sure if that is all this question is asking for, but thank you nevertheless =)