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Homework Help: Total Internal Reflection

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the lowest angle of θ1 given the apex angle is 60°. Air (n=1) is on the outside and inside (n=1.5)


    ϕ is defined as 60 degrees.

    2. Relevant equations

    3. The attempt at a solution

    θc = sin-1([itex]\frac{1.00}{1.50}[/itex]) = 41.81°

    To my understanding, θ1 must angle in such a way to make r (the angle of refraction) to be equal to the critical angle. At this point you will start having TIR.

    They state that r = ϕ + θc
    How? I am not seeing it.

    Once I found r, I can just use snells law to find θ1 - but I don't understand how to find r.
    Last edited: Apr 18, 2012
  2. jcsd
  3. Apr 18, 2012 #2


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    Need some sort of diagram so the position of this θ1 is knows.
    Last edited by a moderator: May 5, 2017
  4. Apr 18, 2012 #3
    I give one but perhaps its not showing for you since its minus.com, here it is on imgur

  5. Apr 18, 2012 #4


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    Image came through that time.

    If you look at the top triangle - the one with the 60o angle, the other two angles are (90 - r)o and (90 - θc)o

    That means [(90-r) + ϕ + (90-θc)] = 180

    so 180 -r + ϕ - θc = 180

    or -r + ϕ - θc = 0 which means r = ϕ - θc

    Notice that is slightly different to what was in your original solution. I suspect something was wrong.
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