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

Answer 1

Answer: (B)

Image formation by a mirror (eitherplane 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 the liquid in the tank,
apparent depth of $P=x_{1}=\frac{d-h}{\mu}$,
apparent depth of the image of $P=x_{2}=\frac{d+h}{\mu}$,
apparent distance between $P$ and its image $=x_{2}-x_{1}=\frac{2 h}{\mu}$.