Question

A container of depth H is filled with two immiscible transparent liquids of refractive indices ${\mu }_1$, and ${\mu }_2$ respectively. The depth of each type of liquid is $\frac{H}{2}$. When viewed from above, the apparent depth of the vessel is

• A. $\frac{H}{2}[\frac{1}{{\mu }_1}+\frac{{\mu }_1}{{\mu }_2}]$
• B. $\frac{H}{2}[\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}]$
• C. $H[\frac{1}{{\mu }_1}+\frac{{\mu }_1}{{\mu }_2}]$
• D. $\frac{H}{2}\left[\frac{{\mu }_1{\mu }_2}{{\mu }_1+{\mu }_2}\right]$

Answer 1

The correct option is A $\frac{H}{2}[\frac{1}{{\mu }_1}+\frac{{\mu }_1}{{\mu }_2}]$

Apparent depth of first liquid $=\frac{H}{2{\mu }_1}$

Apparent depth of second liquid $=\frac{H}{2\left({\mu }_1/{\mu }_1\right)}$

$\therefore$ Total apparent depth $=\frac{H}{2{\mu }_1}+\frac{H{\mu }_1}{2{\mu }_2}$

$=\frac{H}{2}[\frac{1}{{\mu }_1}+\frac{{\mu }_1}{{\mu }_2}]$