Q 12-09-175JEE MainJEE Main 2020 (9 Jan, Shift 1)Easy
A vessel of depth $2h$ 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 the vessel will be
Answer: (D) $\dfrac{3\sqrt{2}\,h}{4}$
Viewed from above (near-normal), each layer appears shortened by its own refractive index:
$$d_{\text{app}} = \frac{h}{\sqrt{2}} + \frac{h}{2\sqrt{2}} = \frac{3h}{2\sqrt{2}} = \frac{3\sqrt{2}\,h}{4}$$
Solution by Sreeraj P, M.Sc Physics