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Homework Help: Destructive interference in wavelengths question

  1. Jan 22, 2007 #1
    1. A nonreflective coating (n = 1.24) covers the glass (n = 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum = 564 nm), determine the minimum nonzero thickness that the coating can have.

    2. wavelength of the light in the coating = wavelngth of light / n of coating

    desructive interference: 2t = (1,2...) wavelngth coating

    3. OK the wavelngth of the light through the coating is: 564/1.24 = 454.84

    I figured maybe that was all i needed and attempted to find t.

    t= 227.42

    this was not correct, so I next proceded to find the wavelength once through the film to the glass:

    454.84/1.52 = 299.24 nm

    The destructive interference for this is:

    2t = (1) 299.24
    t= 149.62 nm

    This too was incorrect.

    I even tried plugging in the original wavelength of 564 nm with the n of glass; 1.52, then solving for t. This gave me:

    564/1.52 = 371.05
    2t= (1) 371.05
    t= 185.53

    None of these were correct.

    Any thoughts on where am I going wrong?
  2. jcsd
  3. Jan 22, 2007 #2
    I think I've made some progress:

    Since there are 2 1/2 wave shifts then the equation should be:

    2t + 1 wavelength in film = (1/2) wavelength in film

    this gave me an answer of 341.13 nm for t and is still incorrect though.
  4. Jan 22, 2007 #3
    Ok nevermind I finally figured it out. I was adding the wave shift across the sides of the formula rather than subtracting it like I should have.

    Thanks to those who considered it for me though. :smile:
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