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posted by  rotnac on 11/7/2009 12:26:56 PM  |  status: Closed  |  Earned Karma: 35

Nonreflective Coating

Course Textbook Chapter Problem Needs by
Algebra Based Physics Physics (7th) by Cutnell, Johnson 27 CQ #6 11/9/2009 at 12:00:00 PM
Question Details:
A camera lens is covered with a nonreflective coating that eliminates 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 it were 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 travel farther through the coating when incident at 45°.  I'm not sure how to justify my answer.
***Please do not post the poor answer that is already available for this problem.
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posted by Physics-Ga on 11/7/2009 4:33:27 PM  |  status: Live
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Response Details:
n d = (k + 1/2) λ / 2     the optical thickness of the film is and odd number of 1/4 λ for destructive interference
                                      where n for the lens > n for film so there is a phase change at both surfaces
If k = 1 then n d = λ / 4
Let L be the optical path at ˜ 45 deg
Then L sin 45 = 2 n d = λ / 2   for the total path length thru the film
So L = .7 λ    and there would only partial interference
Suppose the total path length were 3.5 λ (destructive interference) then L = 4.95 λ
which would give constructive interference.
It's probably difficult to get a film of only λ / 4 thickness so the answer would depend on the actual thickness of the film
so in general one would not expect to get destructive interference except for particular film thicknesses.
(Suppose the direct path length thru the film is 14.5 λ   then L ˜ 20.5  λ   and you get cancellation)
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