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Thin films: reflection between glass plates

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  1. Apr 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Two parallel glass plates of index of refraction n
    are separated by an air film of thickness d. Light of wavelength λ
    in air, normally incident on the plates, is intensified
    on reflection when, for some integer m

    a) 2d=mλ
    b) 2d=mλ/n
    c) 2d=mnλ
    d) 2d=(m+1/2)λ
    e) 2d=mλ/2

    2. Relevant equations
    If only one ray is π shifted: 2nd=mλ (min), 2nd=(m+1/2)λ (max)

    If both rays π shifted: 2nd=mλ (max), 2nd=(m+1/2)λ (min)

    3. The attempt at a solution
    I've attached a diagram of two different for how I picture light should be transmitted in this problem. I'm not sure which one would be a correct approach.

    Going with the first diagram,
    This would result in a net π shift, so it's conditions would be 2nd=mλ (min) and 2nd=(m+1/2)λ (max).

    I chose answer (B) 2d=mλ/n, since the question asks for "intensity increase" so I am assuming it is asking about the condition for a bright fringe; and also because it's one of the only options that takes the index of refraction (n) into account.

    I would just like to verify that my reasoning is correct.
     

    Attached Files:

    Last edited: Apr 24, 2016
  2. jcsd
  3. Apr 24, 2016 #2

    ehild

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    You are wrong . The light interference happens because of multiple reflection inside the thin air film between the thick glass plates. d is the thickness of the air film. n is the refractive index of the glass. You can consider the set-up that the air film is surrounded by glass and the light arrives to the glass-air boundary from glass, and reflected from the other side of the air film, from glass.

    The
     
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