What is the Phase Change for Reflection Between Different Refractive Indices?

[Monochr]

Homework Statement

Part of a longer question, what is the phase change, if any for a system of three substances of different n where there is surface reflection between n1 and n_f which is meant to constructively interfere with another surface reflection between n_f and n3.where n1 < n_f > n3 with n3 > n1?

Homework Equations

None, the textbook I am using only says that when n1 = n3 there will be a pi phase change and there will be none if n1>n_f>n3 or n1<n_f<n3.

The Attempt at a Solution

None, other than an intelligent guess it will be some sort of function with 0 < f(n_f) < pi.

 

[Monochr]

Anyone? This is part of a much larger project and I can well assume that it is indeed pi, the point is that I don't want to make too many undue assumptions.

 

[michalll]

When a light reflects on a material with higher refractive index it undergoes a phase change of pi in the other case the phase does not change, in your case there will be a pi change on n1, nf and no change at nf ,n3 so the phase change must be pi otherwise the interference would be destructive.