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Homework Help: Question regarding optics(prism)

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data

    figure shows a 90 degrees triangular prism of refractive index n whereby light enters at point A with an incident angle of θ. The light then refracts at point B with an angle of refraction of 90 degrees.

    determine index of refraction, n in terms of θ. refer to figure attached.


    2. Relevant equations

    using snell's law of refraction,

    n.sinθ=n1.sinθ1

    3. The attempt at a solution

    first I used an snell's law to get an eqn

    1.sinθ=n.sinθ1----------------------(1)

    using properties of angles and triangles I got
    θ2, θ3 and θ4.
    θ1=θ3, θ2=θ4.

    using snell's law again I got
    n.sinθ4=1.sin 90 degrees
    n.sinθ4=1

    I tried using trigonometry to compute the thetas together and eventually eliminate θ1. But I was not able to do so. Am I missing something?
    Since I got stuck, I thought if θ1=45 degrees, getting n in terms of θ is not a problem. But I reasoned to myself that it cannot be possible as I do not know θ4 and n. So making an assumption is not right. I think? I could be wrong though.. hmm..

    help would be greatly appreciated and I am sorry if posted anything wrongly such as the format or thought process since this is the first time I am posting.

    Thanks!!

    Syeh
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sep 18, 2010 #2

    kuruman

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    You have two equations

    sinθ = n sinθ1
    n sinθ4 = 1

    Can you find a relation between θ1 and θ4?
     
  4. Sep 19, 2010 #3
    hmm.. thanks for replying.. I went through that before.. basically 1=ncosθ1 since 90 degrees-θ4=θ1=θ3. and if i were to combine both eqns together, it will result in

    sinθ=tanθ1.

    the thing is I couldnt eliminate θ1 but I eliminated n instead. I even tried substituting other values of relevant θ into the equation and it got me more irritated. It feels like Im missing something right before my eyes and I cannot comprehend what is it that I missed. oh man. Anyway, this qns is the first part of a 4 parts 12 marks qns. So the solution shouldnt be too complicated. Thanks for replying again.
     
  5. Sep 19, 2010 #4

    ehild

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    So cosθ1=1/n. What is sinθ1 in terms of n?

    ehild
     
  6. Sep 19, 2010 #5
    oh my. hahaa. thanks for making me rethink the qns. i managed to n in terms of theta. thanks again!!! : D
     
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