A point source of light is 150 m below the surface of a body

A point source of light is 1.50 m below the surface of a body of water. Find the diameter of the circle at the surface through which light emerges from the water.

Solution

The cone of light coming from the source will be visible ( as a circle ) as far out as the angle of incidence is less than the critical angle

Critical angle = sin ^–1 ( 1 / 1.33 ) = 48.75

Now, let us consider R is the radius of cone which appears as a circle from top.

Then,

R = (1.5)Tan(48.75) = 1.710 m

So, the volume of the required cone = (1/3)pi*R^2*h = (1/3)*3.14*1.710^2*1.5 = 4.59 m^3