Question

A girl sees through a circular glass slab(refractive index $1.50$ of thickness $20mm$ and diameter $60cm$ 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. $100m^2$
• B. $160m^2$
• C. $190m^2$
• D. $220m^2$

Answer 1

Answer: (B)

$160m^2$

For maximum possible area I should be ${90}^o$.

Now $Sin90=\frac{4}{3}sinr\to sinr=\frac{3}{4}$

$tanr=\frac{3}{\sqrt{7}}$

now the radius of base visible is $r=\frac{0.6}{2}+6\times tanr$

base area $A=\pi r^2=160m^2$