Question

A container is filled with water (μ = 1.33) up to a height of 33.25 cm. A concave mirror is placed 15 cm above the surface of water, as shown in the Fig. The image, of an object O, at the bottom gets formed at I, 25 cm below the water level. The focal length of the mirror is (approximately)

(1) 10 cm

(2) 15 cm

(3) 20 cm

(4) 25 cm

Answer 1

(3) 20 cm

Due to refraction at water, the object, at O, appears to be at a distance of 33.25/1.33 cm ≃ 25 cm , below the top level of water. 

Hence the object distance for mirror = (25+15) cm = 40 cm

For concave mirror

u = -40 cm, v = -b (say), f = ?

However, the reflected rays again undergoes refraction at surface of water. The apparent depth of the image, below the water level in tank, is μb' and is given to be 25 cm. Therefore,