How Is the Longest Wavelength of Light Determined for Anti-Reflective Coatings?

[Barry Melby]

Homework Statement

A sheet of glass (nglass = 1.5) is coated with a 95.6-nm-thick layer of magnesium fluoride (ncoating = 1.38) to prevent reflection in the visible spectrum. Assume the incoming light is normal to the surface.
What is the longest wavelength of light strongly reflected from this coated surface?

Homework Equations

The Attempt at a Solution

95.6 = x/4(1.38) = 527 nm
This is incorrect however.

 

[Simon Bridge]

Please show your reasoning.
Note: you have written 95.6 = 527 ... which is, indeed, false. I don't think that is what you meant.

Under what circumstances does a reflected wave invert?
What condition is needed for strong reflection off the top surface of the film?