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Effective Refractive Index - Should be simple

  1. Oct 20, 2012 #1
    Imagine a dielectric made of of alternating layers of widths A and B and refractive indices (a*) and (b*). Find the effective refractive index, N

    So in general: c/n = wavelength x frequency = phase speed

    My thinking was find the total time taken for the wave to propagate through the distance A+B and work out the refractive index from this.

    So,

    Time=distance/speed = (A+B)/(c/N) = (A/(c/a*)) +(B/(c/b*))

    But this gives me the wrong value for N

    The answer I'm looking for is N^2= [A(a*)^2 + B(b*)^2]/(A+B)

    Where am I going wrong?
     
  2. jcsd
  3. Oct 20, 2012 #2
    Is it that I need to use the optical path length..ie refractive index x physical length in my calculations? That will make it work I think but can someone explain why...
     
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