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Interference in Thin Films, figuring out the phases

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data
    I don't have a question on a specific problem, I am more caught up in the determination of the phases- I'll give a general problem to use as an example:

    In Fig. 35-41, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. The waves of rays r1 and r2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). We are given:

    n1=1.32
    n2=1.75
    n3=1.39
    we want to find a max
    for the 3rd least thickness of L (in nm)
    λ=382nm (in air)

    Figure: nt0043-y.gif

    rays are tilted for clarity

    2. Relevant equations
    Since we want a maximum, the general equation for a maximum would be:
    2L=(m+1/2)λ/n2


    3. The attempt at a solution

    in the case of this problem, we add an additional λ/2 for the incidence of r1 on n2.
    so my real question is this-

    why is it that you multiply m by 2 to end up with 2m+1 in this case? when do you just use (m+1)λ vs (2m+1/2)λ


    I've been reading and researching for hours now, so any help would truly be appreciated.
     
  2. jcsd
  3. Nov 20, 2011 #2

    Simon Bridge

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    High-speed to slow speed you get a phase inversion.
    http://www.kettering.edu/physics/drussell/Demos/reflect/reflect.html [Broken]
    ... it has neat animations of the effect for string, you have to scroll down for the general.

    That 2m+1 gives you an odd number - do you see why an odd number is needed?

    The trick is to try drawing a wave as it propagates through the film. What happens if it's an even number?
     
    Last edited by a moderator: May 5, 2017
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