Water in a pond appears to be only three-quarters of its actual depth.

(a) What property of light is responsible for this observation? Illustrate your answer with the help of a ray diagram.

(b) How is the refractive index of water calculated from its real and apparent depths?

(a) Water in a pond appears to be only three-quarters of its actual depth due to the refraction of light while travelling from one medium to another.

The light rays suffer refraction while travelling from denser medium (water or glass) to rarer medium (air), so it bends away from the normal. Below is the ray diagram for this:

(b) Let us say an object (B) is at the bottom of a pond. Consider a ray of light BC from the object that moves from water to air.

The ray now moves away from the normal N along the path CD, after refraction from the water surface.

When we produce CD it appears from the point B’.

The virtual image of the object B appears at B’.

Hence, we get,

$\text {Refractive index of water} = \dfrac {\text {Real depth}}{\text {Apparent depth}} \\[0.5em]$