Question

Water in a pond appears to be only three-quarter 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 the refractive index of water calculated from its real and apparent depths? [3 marks]

Answer 1

(a) 'Refraction of light' is responsible for this property. [1 mark]

(b) When light coming from denser medium enters the rarer medium, it is bent away from the normal.

Let any object B is at the bottom of a pond. Consider a light ray BC from the object that moves from water to air. After refraction from the water surface, the ray moves away from the normal N along the path CD. The produce of CD appears from the point B' and a virtual image of the object at B appears at B'.

The pond appears to be three-quarters of its actual depth due to the property of refraction of light.

​​​​​​Refractive index $\mu =\frac{\text{Real depth}}{\text{Apparent depth}}$

Since $\mu =\frac{4}{3}$ for water

Therefore, Apparent depth = $\frac{4}{3}\times$ Real depth [2 marks]