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Deriving an expression from geometry

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data

    I need to derive an expression for the displacement of light as a function of thickness of glass and the angles.

    I will post a screen shot of the formula to be derived but it can also be found here

    http://clas.wayne.edu/multimedia/usercontent/File/Physics%20and%20Astronomy/Labs/PHY5341/Lab4%20Brewsters%20Angle.pdf [Broken]

    (pg 3)

    2. Relevant equations

    The equation is given as the solution. I am not very good with geometry so I don't really even know where to begin.

    3. The attempt at a solution

    Using Snell's law,

    n1sinθ1=n2sinθ2

    Solving for θ2 = Arcsin[(n1/n2)sinθ1]

    So then I just have θ2.

    Help, please?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 17, 2013 #2

    ehild

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    See attachment. You have to find the expression for the distance (d) between the original ray (1) and the displaced one (2). t is the thickness of the slab. There are two right triangles in the picture, with common hypotenuse (s ). Find s in terms of t and θ2, find d in terms of s and θ21. Eliminate θ2.

    ehild
     

    Attached Files:

  4. Feb 17, 2013 #3
    Thanks a lot for your help mate. I tried this problem for about an hour and I'm completely stuck. I never went to high school to get that Euclidian intuition and I'm dyslexic so I don't have a good geometric intuition. I'm just stuck, I can't see the solution in sight.

    But I thank you for your assistance very much.
     
  5. Feb 18, 2013 #4

    ehild

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    Do you see the right triangles in the picture? What is the relation between t, s and θ2?

    What is the angle of the blue triangle between side s and the hypotenuse?


    ehild
     

    Attached Files:

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