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Homework Help: Thin film interference

  1. Dec 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Light of wavelength [tex]\lambda[/tex] = 500nm, produced by an extended source, is incident at an angle of [tex]\phi[/tex]= 30 degrees from the normal upon a dielectric film of refractive index, n=2, supported on a solid planar substrate. Reflectivity minima are observed to have an angular separation of 0.05 radians. What is the thickness, d, of the film?

    2. Relevant equations

    Phase difference [tex]\delta[/tex] = 2ndcos[tex]\theta[/tex]*(2*pi/[tex]\lambda[/tex]) where sin[tex]\phi[/tex]=nsin[tex]\theta[/tex]

    Intensity proportional to sin2([tex]\delta[/tex]/2)



    3. The attempt at a solution

    0th and first minima occur when the [tex]\delta[/tex]=0 and [tex]\delta[/tex]=2 pi respectively.

    Hence:
    2ndcos[tex]\theta[/tex]*(2*pi/[tex]\lambda[/tex]) = 2pi

    which gives d=258nm

    which seems very small and I didn't have to use the angular seperation to get my answer which leads me to believe I'm doing something wrong.

    I think my mistake is to do with the fact I don't now how to involve the angular separation of 0.05 radians into the solution?

    Help appreciated
     
  2. jcsd
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