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Thin-film interference question

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data
    The table lists the range of wavelengths in vacuum corresponding to a given color. If one looks through a film which has a refractive index of 1.333 and thickness of 340 nm (nanometers), which color will be 100% transmitted through the film?

    Table (Color/Wavelength):
    • red/780nm-622nm
    • orange/622nm-597nm
    • yellow/597nm-577nm
    • green/577nm-492nm
    • blue/492nm-455nm
    • violet/455nm-390nm

    A) red
    B) yellow
    C) violet
    D) green
    E) white

    2. Relevant equations
    refractive index of air is 1, so n(air)<n(film)>n(air) condition is met. relevant equations will be:
    [tex]t(min)=\frac{\lambda}{2*n(film)}[/tex]

    where n(film) is the refractive index of the film and t(min) is minimum film thickness

    3. The attempt at a solution
    I tried this problem, making n(film)=1.333 and t(min)=340 nm, solving for [tex]\lambda[/tex].
    I got [tex]\lambda[/tex]=2*n(film)*t(min)=2*1.333*340=906nm
    However, this exceeds the wavelength for any of the colors, and the answer should be (C). What did I do wrong?
     
  2. jcsd
  3. Apr 14, 2010 #2

    ehild

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    You get maximum transmittance through the film if its thickness is any integer multiple of lambda/(2n)



    ehild
     
  4. Apr 15, 2010 #3
    yeah, but how do you come up with the correct wavelength?
     
  5. Apr 15, 2010 #4

    ehild

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    Find the possible wavelengths which are between 780nm and 390 nm. All of them are correct.

    ehild
     
  6. Jul 6, 2010 #5
    how this relationship between thickness, refractive index and wavelength is obtained? is there any relationship between complex refractive index with film thickness?
     
  7. Jul 6, 2010 #6
    Uhh, I don't think so. The refractive index depends on the material the medium is made of, and that's it. What I was asking here was an interference question. When the medium is at a certain thickness, the light reflected from one end of the medium interferes with that from the other end to cancel each other out.
     
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