Question

A point source of light is 20 cm below the surface of water . Find the diameter of largest circle at the surface ,through which light can emerge from the water.

Answer 1

it is based on concept of critical angle .
when R is the radius of largest circle at the surface , C is the critical angle.
then, R = 20tanC.

so, we have to find critical angle at first.
we know, from Snell's law,
$sinC=\frac{1}{\mu}$
here $\mu$ refractive index of water e.g., 4/3
so, $sinC=\frac{3}{4}$
hence, $tanC=\frac{3}{\sqrt{7}}$
now, R = 20tanC = 20 × 3/√7
= 60/√7
so, diameter = 2 × 60/√7 = 120/√7 = 45.35m