An empty tank has a concave mirror as its bottom. When sunlight falls normally on the mirror, it is focussed at a height of 32 cm from the mirror. If the tank is filled with water upto a height of 20 cm, then the sunlight focuses at ( refractive index of water $=\frac{ 4}{3}$)

Sun is at infinity i.e. u = ∞ so from mirror formula we have

$\frac{1}{f}=\frac{1}{-32}+\frac{1}{(-\infty )}\Rightarrow f=-32 \mathrm{cm}$

When water is filled in the tank upto a height of 20 cm, the image formed by the mirror will act as virtual object for water surface. Which will form it’s image at such that 
$\frac{\text{ Actual height }}{\text{ Apperant height }}=\frac{{\mu }_{\mathrm{w}}}{{\mu }_{\mathrm{a}}}$

$\frac{\mathrm{BO}}{\mathrm{BI}}=\frac{\frac{4}{3}}{1}\Rightarrow \mathrm{BI}=\mathrm{BO}\times \frac{3}{4}=12\times \frac{3}{4}=9 \mathrm{cm}$