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Find the angle of incidence

  1. Aug 22, 2014 #1
    1. The problem statement, all variables and given/known data

    A ray of light incident on a glass sphere (refractive index sqrt 3) suffers total internal reflection before emerging out exactly parallel to the incident ray. What was the angle of incidence?

    μ = refractive index of the glass sphere, i = angle of incidence, r = angle of refraction

    2. Relevant equations

    μ = sin i/sinr

    3. The attempt at a solution

    From the figure, it turns out that < AOE = i (since L1 is parallel to L2, the corresponding angles are equal)

    i = 2r, which implies that sin i/ sinr = μ, or 2cosr = μ, or r = 30° and i = 60°, which is the answer.

    I do not understand why < ABO = r. Why is it so? It'd be helpful if I someone could come up with a different way of approaching the problem.
     

    Attached Files:

  2. jcsd
  3. Aug 22, 2014 #2

    haruspex

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    Isosceles triangle (two radii).
     
  4. Aug 22, 2014 #3

    Simon Bridge

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    ΔABO is an isosceles triangle: |OA|=|OB|

    [edit] beaten to it :)
     
  5. Aug 23, 2014 #4
    Oops! I ought to have thought a bit more before posting that question. Thank you. :)
     
  6. Aug 23, 2014 #5

    Simon Bridge

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    No worries. Everyone does it sometimes :)
    You'd probably have noticed right away if the diagram was constructed rather than sketched, even though you noticed about the equal base-angles.
     
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