Q 12-09-102JEE MainJEE Main 2024 (31 Jan, Shift 2)Medium
Light from a point source in air falls on a convex curved surface of radius $20\ \text{cm}$ and refractive index $1.5$. If the source is located at $100\ \text{cm}$ from the convex surface, the image will be formed at ______ cm from the object.
Numerical value type. Enter your answer.
Answer: 200
$$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}:\qquad \frac{1.5}{v} + \frac{1}{100} = \frac{0.5}{20} = \frac1{40}$$
$$\frac{1.5}{v} = \frac1{40} - \frac1{100} = \frac{3}{200} \Rightarrow v = 100\ \text{cm}$$
The image is $100\ \text{cm}$ inside the surface, so its distance from the object is $100 + 100 = 200\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics