A point source of light is 96.7 cm below the surface of a body of water. Find the diameter of the circle at the surface through which light emerges from the water. Water has an index of refraction of 1.33.

Answer 1

There is a maximum angle that a ray from the source can have with the vertical, and not be totally reflected. That angle is called the critical angle, theta. It is giben by the equation

sin theta = 1/N
where N is the refractive index of water
Therefore theta = 48.7 degrees.

The radius of the circle through which light can escape the water surface, from a depth d below, is

R = d tan theta = 1.14 d

The diameter of the circle is 2R.