Question

A vessel of depth $d$ is half filled with a liquid of refractive index $n_1$ and the upper half is occupied by immiscible liquid of refractive index $n_2$ . Viewing it from an eye in the upper liquid, the apparent depth of the lower liquid is

• A. $\frac{d}{2n_2}$
• B. $\frac{d{n}_1}{2n_2}$
• C. $\frac{d}{2}\left(\frac{n_2}{n_1}\right)$
• D. $\frac{d}{2}\left(\frac{n_1+n_2}{n_1{n}_2}\right)$

Answer 1

Answer: (C)

The depth of the vessel $=d$
Half of the depth $\frac{d}{2}$ of the liquid is filled by liquid of
refractive index of $n_1$.
Upper half, i.e. $\frac{d}{2}$ distance is filled by the liquid of
refractive index $n_2$.

Apparent depth is given by the formula
$=\frac{d(n_1+n_2)}{2(n_1\times n_2)}$
Apparent depth of lower half
$=\frac{d}{2}(\frac{n_2}{n_1})$