A vessel of depth $2 h$ 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 vessel will be

(C) $\frac{3}{4} \mathrm{~h} \sqrt{2}$

(A) $\frac{\mathrm{h}}{\sqrt{2}}$

(B) $\frac{h}{2(\sqrt{2}+1)}$

(D) $\frac{\mathrm{h}}{3 \sqrt{2}}$

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Geometrical Optics

A vessel of depth

2 h

is half filled with a liquid of refractive index

22

and the upper half with another liquid of refractive index

2

. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be

(A) $\frac{h}{2}$
(B) $\frac{h}{2 ( 2 + 1 )}$
(C) $\frac{3}{4} h 2$ ✓ Correct
(D) $\frac{h}{3 2}$

Answer: (C)

Solution

Each liquid layer is

h

deep, and a real depth seen through a medium is reduced by that medium's refractive index. The lower layer, of index

22

, contributes an apparent depth

\frac{h}{2 2}

, while the upper layer, of index

2

, contributes

\frac{h}{2}

. Adding the two, the bottom appears to lie at

\frac{h}{2 2} + \frac{2 h}{2 2} = \frac{3 h}{2 2} = \frac{3 h 2}{4}

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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