Question

A plane mirror is held at a height h above the bottom of an empty beaker. The beaker is now filled with water up to depth $d$. The general expression for the distance from a scratch at the bottom of the beaker to its image in terms of $h$ and the depth $d$ of water in the beaker is :

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

Answer 1

Answer: (C)

$2h-d\left(\frac{\mu -1}{\mu }\right)$

shift observed is $d(1-\frac{1}{\mu })$

object distance wrt mirror is $h-shift=h-d(1-\frac{1}{\mu })$

image distance from mirror is $h-d(1-\frac{1}{\mu })$

distance of image from the scratch at the bottom of beaker is $h-d(1-\frac{1}{\mu })+h=2h-d\left(\frac{\mu -1}{\mu }\right)$

option $C$ is correct