Question

A girl sees through a circular glass slab (refractive index 1.5) of thickness 20 mm and diameter 60 cm to the bottom of a swimming pool. Refractive index of water is 1.33. The bottom surface of the slab is in contact with the water surface.

The depth of swimming pool is 6 m. The area of bottom of swimming pool that can be seen through the slab is approximately

(a) 100 m²

(b) 160 m²

(c) 190 m²

(d) 220 m²

Answer 1

Answer is : (b) 160 m²

Girl can observe only those light rays which are refracted and leaves the glass slab at angle of 90° or less as shown below.

Now, from Snell’s law in layer 1 and 3, we have

Now, from Pythagoras theorem, we have

⇒ tan r = 3/√7

So, from figure, we have

Hence, area of pool visible through glass slab is A = πd²/4 = \(\frac{\pi\times(2x+0.6)^2}{4}\) ≈ 160 m²