Question

Consider the situation shown in figure. A plane mirror is fixed at a height $H$ above the bottom of a container containing oil having $\text{refractive index}\mu$ up to a height $h$. Find the position of the image of the bottom formed by the mirror.

• A.
  $H+h+\frac{h}{\mu }$
• B.
  $H-h+\frac{h}{\mu }$
• C.
  $H+h-\frac{h}{\mu }$
• D.
  $H-h-\frac{h}{\mu }$

Answer 1

The correct option is B

$H-h+\frac{h}{\mu }$
The apparent depth of the container, $d=\frac{h}{\mu }$
$\therefore$ The apparent shift of the bottom, $s=h-d$
$\Rightarrow s=h(1-\frac{1}{\mu })$

So, the apparent distance of the bottom from the mirror is

$=H-s$
$=H-h(1-\frac{1}{\mu })$
$=H-h+\frac{h}{\mu }$
$\therefore$ Image is formed at $H-h+\frac{h}{\mu }$ behind the mirror.

Hence, option (b) is the correct answer.

$\begin{array}{c}\text{Why this question}\\ \text{To understand the meaning of apparent}\\ \text{depth \& apparent shift.}\end{array}$