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Homework Help: Simple Interferometer question

  1. Mar 16, 2006 #1
    I've been doing some working with a michelson interferometer, specifically finding the refractive index of a glass block. I am given this eqn:

    n = (2t-ML)(1-cos)/ (2t (1 - cos) - mL)

    Where n is the refractive index of the glass
    M is number of fringes passing
    I have left the thetas out becuase they mess up how it looks but u can assume cos = cos theta1.
    t is thickness of the glass
    L is Lambda the wavelength of the light.

    I am trying to prove this eqn.

    Here is what I have.

    I know that the optical path length is the distance the light travels in the glass * n.

    Where B is the distance travelled in the glass B = t cos theta2

    Theta1 is angle of incidence, theta 2 is angle of refraction.

    From elsewhere L = 2d/M

    In this case B will be my d as this is the distance that the beam travel in excess of its normal path.

    Now I have tried just shoving everything in and hoping I can simplify it but to no avail. How should I be going about this?
  2. jcsd
  3. Mar 12, 2007 #2


    You know what, we have the same problem. I'm also trying to simplify it. I'm using a backward approach. But I still can't find it. But anyway, if i'm gonna be able to derive it totally, I'll just send it to you.
  4. Mar 13, 2007 #3
    Not entirely sure I follow (sketch would help), but where do you get L=2d/M? B=tcos(theta2), but if I understand your problem then this is the path within the glass, not the distance the beam travels in excess of it's "normal" path.
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