A camera lens is covered with a nonreflective coating thateliminates the reflect

Question

A camera lens is covered with a nonreflective coating thateliminates the reflection of perpendicularly incident green light.Recalling Snell’s law of refraction (see Section 26.2),would you expect the reflected green light to be eliminated if itwere incident on the nonreflective coating at an angle of 45°rather than perpendicularly? Justify your answer.
I figured that light would not be eliminated because it must travelfarther through the coating when incident at 45°. I'm notsure how to justify my answer. ***Please do not post the poor answer that is alreadyavailable for this problem. A camera lens is covered with a nonreflective coating thateliminates the reflection of perpendicularly incident green light.Recalling Snell’s law of refraction (see Section 26.2),would you expect the reflected green light to be eliminated if itwere incident on the nonreflective coating at an angle of 45°rather than perpendicularly? Justify your answer.
I figured that light would not be eliminated because it must travelfarther through the coating when incident at 45°. I'm notsure how to justify my answer. ***Please do not post the poor answer that is alreadyavailable for this problem.

Explanation / Answer

n d = (k + 1/2) / 2     the opticalthickness of the film is and odd number of 1/4 fordestructive interference                                      where n for the lens > n for film so there is a phase change atboth surfaces If k = 1 then n d = / 4 Let L be the optical path at ˜ 45 deg Then L sin 45 = 2 n d = / 2   for the totalpath length thru the film So L = .7     and there would onlypartial interference Suppose the total path length were 3.5 (destructiveinterference) then L = 4.95 which would give constructive interference. It's probably difficult to get a film of only / 4thickness so the answer would depend on the actual thickness of thefilm so in general one would not expect to get destructiveinterference except for particular film thicknesses. (Suppose the direct path length thru the film is 14.5   then L ˜ 20.5    andyou get cancellation)

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