Optics: Total internal reflection problem

[viny]

Homework Statement

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

Homework Equations

Total internal reflection: θ_c = sin^-1 n_(air)/n_(water)

The Attempt at a Solution

I've found that the critical angle is θ_c = 48.75. However, I cannot seem to find the similar triangles required to find the distance.

 

[Doc Al]

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).