Q. Each quarter of a vessel of depth $H$ is filled with liquids of the refractive indices $n_{1},\ n_{2},\ n_{3}$ and $n_{4}$ from the bottom respectively. The apparent depth of the vessel when looked normally is
A) $\frac{H\left( n_{1} + n_{2} + n_{3} + n_{4} \right)}{4}$
B) $\frac{H\left( \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + \frac{1}{n_{4}} \right)}{4}$
C) $\frac{\left( n_{1} + n_{2} + n_{3} + n_{4} \right)}{4H}$
D) $\frac{H\left( \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + \frac{1}{n_{4}} \right)}{2}$
Explanation
(b) Apparent depth of bottom
$= \frac{H/4}{\mu_{1}} + \frac{H/4}{\mu_{2}} + \frac{H/4}{\mu_{3}} + \frac{H/4}{\mu_{4}}$
$= \frac{H}{4}\left( \frac{1}{\mu_{1}} + \frac{1}{\mu_{2}} + \frac{1}{\mu_{3}} + \frac{1}{\mu_{4}} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.