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{dn_{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})$