Question

A plane mirror is placed at the bottom of the tank containing a liquid of refractive index $n$. 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. $2nh$
• B. $\frac{2h}{n}$
• C. $\frac{2h}{n-1}$
• D. $h(1+\frac{1}{n})$

Answer 1

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

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 $P=x_1=\frac{d-h}{n}$

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

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