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Problem on optics

  1. Jun 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Light falls on the surface AB of a rectangular slab from air. Determine the smallest refractive index n that the material of the slab can have so that all incident light emerges from the opposite face CD.
    upload_2015-6-9_20-39-0.png

    2. Relevant equations


    3. The attempt at a solution
    Let's think about this case:
    upload_2015-6-9_20-49-45.png
    There must be total internal reflection at Q and S.
    That means, ##90-r>\theta _c## [##\theta _c## is the critical angle]
    ## sin(90-r)>sin \theta _c##
    ##cos r > \frac{1}{n}## [## sin \theta _c = \frac {1}{n}##]
    ##n>sec(r)##
    But, the maximum value of ##sec(r)## is infinite.
    That means n should be infinite.
    But that is not the answer.
     
  2. jcsd
  3. Jun 9, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    Try it again. Write down the maximum ##r## in terms of arc-sin of something. Write down ##\theta_C## in terms of arc-sin of something. Then write down ##90-r > \theta_C## in terms of these arc-sin formulas. Don't forget that air has an index of refraction very close to 1. See what you get.
     
  4. Jun 9, 2015 #3
    I have got the answer. :)
     
  5. Jun 9, 2015 #4
    ..
     
    Last edited: Jun 9, 2015
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