Question

A vessel is half filled with liquid of refractive index n.The other half of the vessel is filled with an immiscible liquid of refractive index 1.5n.The apparent depth of the vessel is 50% of the actual depth.Then n is a)1.4 b)1.5 c)1.6 d)1.67

Answer 1

Expression for refractive index:

$\mu =\frac{Realdepth}{Apparentdepth}$

Half filled with refractive index n:

Apparent depth $=\frac{Realdepth}{n}$
=$\frac{d/2}{n}$
$=\frac{d}{2n}$

Other half filled with refractive index 1.5n:

Apparent depth $=\frac{Realdepth}{1.5n}$
$$\begin{gathered} =\frac{d/2}{1.5n} \\ =\frac{d}{3n} \end{gathered}$$

Total apparent depth:

$$\begin{gathered} Totalapparentdepth=\frac{d}{2n}+\frac{d}{3n} \\ =\frac{5d}{6n} \end{gathered}$$

But, total apparent depth is d/2.

Hence,

$$\begin{gathered} \frac{5d}{6n}=\frac{d}{2} \\ 6n=10 \\ n=\frac{10}{6} \\ =\mathbf{1}\mathbf{.}\mathbf{67} \end{gathered}$$