Thin Film Interference: How does Maxwell's Equations Explain?

physicsnoob93
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Not really a homework problem. Just wanted to know:

When light moves from a medium of lower index of refraction to that of a higher index of refraction, the reflected ray suffers a phase change. (Thin film interference)

But the other way round, this doesn't happen. This can be shown by maxwell's equations according to my physics text. But how?!

If somebody could show it to me, thank you.
 
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You could always check any E&M textbook from the library or google for it. It would be too much work to explain here so here is a link from a simple google search:

http://www.usna.edu/Users/physics/mungan/Scholarship/PhaseChange.pdf

You can find many more like that.
 
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