Question

A concave mirror of radius of curvature $60\text{cm}$ is placed at the bottom of a tank containing water up to a height of $20\text{cm}$. The mirror faces upwards with its axis vertical, solar light falls normally on the surface of water and the image of the sun is formed. If $\mu =4/3$ for water, then with the observer in air, the distance of the image from the surface of water is

• A. $30\text{cm}$
• B. $20\text{cm}$
• C. $7.5\text{cm}$ below
• D. $7.5\text{cm}$ above

Answer 1

The correct option is D $7.5\text{cm}$ above

Given:
$R=60\text{cm}$

$f=\frac{R}{2}=\frac{60}{2}=30\text{cm}$



Image of the sun will be formed at focus of the concave mirror.

So, Real height $h_r=30-20=10\text{cm}$

Refractive index $\left(\mu \right)$ can be defined as

$\mu =\frac{\text{Real depth}}{\text{Apparent depth}}=\frac{h_r}{h_a}$

$\Rightarrow h_a=\frac{h_r}{\mu }=\frac{10}{\mu }$

$\Rightarrow h_a=\frac{10}{4/3}=7.5\text{cm}$ above water surface.

Hence, option $\left(d\right)$ is correct.