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Solving index of refraction for Total Internal Reflection

  1. Mar 18, 2015 #1

    RaulTheUCSCSlug

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    1. The problem statement, all variables and given/known data
    Screenshot 2015-03-18 at 7.00.08 PM.png

    2. Relevant equations
    Snell's Law
    n1sin(theta_1)=n2sin(theta_2)
    Total Internal Refraction:
    sin(theta_c)=(n_2/n_1)

    lambda_n=lambda_n

    3. The attempt at a solution

    So I drew the triangle and this is what I got, and well here is just a picture so far of what I have. impossibleprobleeem.jpg


    I've done this problem before and got n=(theta)-(arcsin((sin(theta)/n)) and from there I have no idea. But I did a different approach. Any ideas. I've tried differentiating implicitly after that and trying to integrate and just got a huge mess.
     
  2. jcsd
  3. Mar 18, 2015 #2

    ehild

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    Show your work in readable form.
     
  4. Mar 18, 2015 #3

    RaulTheUCSCSlug

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    I just wrote down what I know and some equations, I found out the angle of refraction when the laser beam first enters. But I don't know what to do after.
     
  5. Mar 18, 2015 #4

    ehild

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    Find the angle of incidence at S2.
     
  6. Mar 18, 2015 #5

    RaulTheUCSCSlug

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    It would be 90 degrees minus the angle of refraction. But doesn't it have to equal the angle at which it internally reflects?
     
  7. Mar 19, 2015 #6

    ehild

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    Yes, it should be equal or greater than the critical angle, at which internal reflection occurs. But it is not 90°minus the angle of refraction at S1. Give it in terms of theta and the angle of refraction.
     
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