JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Geometrical Optics

When the liquid is poured in, the object at the bottom appears raised because of refraction, the apparent depth being the real depth divided by the refractive index. The microscope must be lifted by exactly the amount through which the object seems to rise, which is the real depth minus the apparent depth. Writing $h$ for the height of the liquid, $h-\frac{h}{\mu }=30\text{ cm}$. With $\mu =\frac{5}{3}$ this becomes $h\left(1-\frac{3}{5}\right)=\frac{2h}{5}=30\text{ cm}$, so the liquid column stands at a height of $75\text{ cm}$.