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Optics: Total internal reflection problem

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    A lamp is placed in the center at the bottom of a 2m deep swimming pool. The lamp emits light in all directions. Starting from a point directly above the lamp, a man in a canoe paddles until he no longer can see the lamp. How far did he paddle the canoe? Assume that the sides of the pool do not reflect light.

    n(water) = 1.33
    n(air) = 1

    2. Relevant equations
    Total internal reflection: θc = sin-1 n(air)/n(water)


    3. The attempt at a solution
    I've found that the critical angle is θc = 48.75. However, I cannot seem to find the similar triangles required to find the distance.
     
  2. jcsd
  3. Sep 25, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You'll want a right triangle. The lamp is the vertex at the bottom and the hypotenuse is a ray from the lamp that hits the water surface at the critical angle (measured from the normal).
     
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