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 above the liquid level sees P and its image in the mirror. The apparent distance between these two will be:

• A. $2\mu \text{h}$
• B. $\frac{\text{2h}}{\mu }$
• C. $\frac{\text{2h}}{\mu -1}$
• D. $\text{h}(1+\frac{1}{\mu })$

Answer 1

The correct option is B

$\frac{\text{2h}}{\mu }$

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 $x_1=\frac{x}{\mu }$ where $x$ is real depth and $\mu$ is refractive index

Apparent depth of $P=x_1=\frac{\text{d-h}}{\mu }$

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

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