Question

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index $\mu$. $P$ is a small object at a height $h$ above the mirror. An observer $O-$vertically above $P$, outside the liquid-sees $P$ and its image in the mirror. The apparent distance between these two will be:

• A. $2\mu h$
• B. $\frac{2h}{\mu }$
• C. $\frac{2h}{\mu -1}$
• D. $h(1+\frac{1}{\mu })$

Answer 1

The correct option is B $\frac{2h}{\mu }$

The P will be formed h distance below the mirror.

Let the apparent depth of P is x₁.

And the apparent depth of image of P is x₂.

So, $x_1=\frac{d-h}{\mu }$

$x_2=\frac{d+h}{\mu }$

Apparent distance between P and its image is

$x_2-x_1=\frac{d+h}{\mu }-\frac{(d-h)}{\mu }$

$=\frac{d+h-d+h}{\mu }$

$=\frac{2h}{\mu }$