Question

A point source of light is placed at a distance h below the surface of a large and deep lake. Show that the fraction f of light that escapes directly from water surface is independent of h and is given by,

Answer 1

Due to TIR, light will be reflected back into the water if i > θ_c. So only that portion of incident light will escape which passes through the cone of angle θ = 2θ_c.

So, the fraction of light escaping

Now, as f depends on θ_c and which depends only on μ, it is independent of h.