Question

A plane mirror is placed at the bottom of the tank containing a liquid of refractive index μ. P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see 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

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

Image formation by a mirror (either plane or spherical) does not depend on the medium.
The image of $P$ will be formed at a distance h below the mirror. If $d$ = depth of liquid in the tank.

Apparent depth of $P=x_1=\frac{d-h}{\mu }$

Apparent depth of the image of $P=x_2=\frac{d+h}{\mu }$

$\therefore$ Apparent distance between P and it's image $=x_2-x_1=\frac{2h}{\mu }$