JEE Physics 2023 Question with Solution

Given: The liquid has refractive index $n = \frac{5}{3}$ and the microscope must be raised by $30 \, \text{cm}$.

Find: The height of the liquid in the bucket.

When an object is viewed through a liquid, its apparent depth is

$$d' = \frac{d}{n}$$

where $d$ is the real depth and $d'$ is the apparent depth.

Since the microscope has to be raised by $30 \, \text{cm}$, the apparent shift is

$$d - d' = 30$$

Substituting $d' = \frac{d}{n}$ and $n = \frac{5}{3}$,

$$d - \frac{d}{\frac{5}{3}} = 30$$ $$d - \frac{3d}{5} = 30$$ $$\frac{2d}{5} = 30$$ $$d = 75 \, \text{cm}$$

Therefore, the height of the liquid is $75 \, \text{cm}$. The correct option is A.

The solution states option D, but the worked calculation gives $75 \, \text{cm}$, which matches option A.