Question

A vessel of depth $2h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

• A. $\frac{h}{\sqrt{2}}$
• B. $\frac{h}{2(\sqrt{2}+1)}$
• C. $\frac{h}{3\sqrt{2}}$
• D. $\frac{3}{4}h\sqrt{2}$

Answer 1

The correct option is D $\frac{3}{4}h\sqrt{2}$

Apparent depth,


The total apparent depth is given by,

$D=\frac{t_1}{{\mu }_1}+\frac{t_2}{{\mu }_2}=\frac{h}{\sqrt{2}}+\frac{h}{2\sqrt{2}}=\frac{3h}{2\sqrt{2}}$
$=\frac{3h\sqrt{2}}{4}$

Hence, $\left(D\right)$ is the correct answer.