Question

A coating of magnesium fluoride MgF2 is often applied to lenses as an anti-reflective coating. It has a refractive index (~ 1.35) between that of air (n=1) and glass (n = 1.5).
a) Compare the phase change at the first surface reflection (air to MgF2), to the phase change at the MgF2 to glass surface reflection. Say individually if they would be in phase (no additional path length) or out of phase (add λ/2 path length).

Note that in calculating correct distances for optical paths to add or cancel, you only need to compensate if the reflections have different phases.
b) If we want to have the reflections from both the air-MgF2 & MgF2-glass surfaces to cancel for light of lambdaVACUUM =560 nm, what is the minimum thickness of the MgF2 coating that is required? c) For optimum results, the reflections at the two surfaces should also be of equal strength (or they won’t cancel completely). In all the preceding questions, we have typically ignored this point.

It can be shown that the strength of reflection depends on the ratio of impedances, so we would like ZAIR/ZMgF2 = ZMgF2/ZGLASS.
Since you know Z = 377/n, what is the optimum refractive index of an anti-reflective coating material?

Answer 1