Q 12-09-238JEE MainJEE Main 2025 (7 Apr, Shift 1)Medium
A container contains a liquid with refractive index $1.2$ up to a height of $60\ \text{cm}$, and another liquid having refractive index $1.6$ is added to height $H$ above the first liquid. If viewed from above, the apparent shift in the position of the bottom of the container is $40\ \text{cm}$. The value of $H$ is ______ cm. (Consider the liquids to be immiscible.)
Numerical value type. Enter your answer.
Answer: 80
Each layer shifts the image by its thickness $\times\left(1 - \dfrac1\mu\right)$:
$$H\left(1 - \frac1{1.6}\right) + 60\left(1 - \frac1{1.2}\right) = 40$$
$$0.375H + 10 = 40 \Rightarrow H = 80\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics