Thin Film Diffraction problem

[klawlor419]

Homework Statement

A broad beam of light, of wavelength 683nm is sent directly down through the top plate of a pair of glass plates. The plates are 120mm long, touch at the left end and are separated by a wire of a diameter .048mm at the right end. Air between the plates act as a thin film. How many bright fringes will be seen by an observer looking down through the top plate?

Homework Equations

Perhaps Snell's Law
Perhaps a calculation for the optical path difference.

The Attempt at a Solution

I am really just not sure where to start with this. I have been plagued by these types of optics questions for a while. I think I basically have to calculate the Optical path difference and that will account for either constructive or destructive interference of the light, with an appropriate wavelength multiple added on to it.

I am not sure why there would be a limit on the number bright fringes seen by the observer looking down at the plates. I guess that is due to the finite size of the plate.

Is it just,
$$2n_{\text{air}}d=m\lambda$$
and solve for m? If so, why?

 

[klawlor419]

I think I need to do an integration summing up the m's for all the values of d. Because the plates go from 0mm separation to .048 mm separation.