question_answer

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 vessel will be                                       [JEE MAIN Held on 09-01-2020 Morning]

A) \[\frac{h}{\sqrt{2}}\]

B) \[\frac{h}{2\left( \sqrt{2}+1 \right)}\]

C) \[\frac{h}{3\sqrt{2}}\]

D) \[\frac{3}{4}h\sqrt{2}\]

Correct Answer: D

Solution :

[d] \[D=\frac{{{t}_{1}}}{{{\mu }_{1}}}+\frac{{{t}_{2}}}{{{\mu }_{2}}}=\frac{h}{\sqrt{2}}+\frac{h}{2\sqrt{2}}=\frac{3h}{2\sqrt{2}}\]