Question

A plane mirror is placed at the bottom of the 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 $\frac{2h}{\mu }$

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 mirror is $=x_2=\frac{d}{\mu }$
$\therefore$ Apparent distance between P and mirror $=x_2-x_1=\frac{h}{\mu }$
$\therefore$ Apparent distance between the image and P is $=\frac{2h}{\mu }$