Q 12-09-232JEE MainJEE Main 2025 (3 Apr, Shift 2)Medium
Light from a point source in air falls on a convex spherical glass surface (refractive index $\mu = 1.5$ and radius of curvature $50\ \text{cm}$). The image is formed at a distance of $200\ \text{cm}$ from the glass surface inside the glass. The magnitude of the distance of the light source from the glass surface is ______ m.
Numerical value type. Enter your answer.
Answer: 4
Light travels from air into glass; take $u = -x$, $v = +200\ \text{cm}$, $R = +50\ \text{cm}$ (centre of curvature inside the glass).
$$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R} \Rightarrow \frac{1.5}{200} + \frac1x = \frac{0.5}{50}$$
$$\frac1x = 0.01 - 0.0075 = 0.0025 \Rightarrow x = 400\ \text{cm} = 4\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics