Question

A girl sees through a circular glass slab(refractive index 1.50 of thickness 20 mm and diameter 60 cm to the bottom of a swimming pol. 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 6m. The area of bottom of swimming pool that can be seen through the slab is approximately.

• A. 100 m${}^2$
• B. 160 m${}^2$
• C. 190 m${}^2$
• D. 220 m${}^2$

Answer 1

The correct option is B

160 m${}^2$

For maximum possible area
I should be 90${}^{\circ }$
1$\times$ $\sin$ 90${}^{\circ }$ =$\frac{4}{3}$ $\sin$ r
$\sin$ r = $\frac{3}{4}$
$\tan$ r =$\frac{3}{\sqrt{7}}$
Total base area $\pi {\left(6\times \frac{3}{\sqrt{7}+0.3}\right)}^2\approx 160m^2$