Light from a point source in air falls on a spherical glass surface of refractive index 1.5 and radius of curvature 50 cm. The image is formed 200 cm from the glass surface inside the glass. Find the magnitude of the object distance from the surface in metres.
Physics · Geometrical optics · refraction due to curved surface
JEE Mains 2025 3 April Evening Shift

Question

Light from a point source in air falls on a spherical glass surface of refractive index 1.5 and radius of curvature 50 cm. The image is formed 200 cm from the glass surface inside the glass. Find the magnitude of the object distance from the surface in metres.

Physics · Geometrical optics · refraction due to curved surface

JEE Mains 2025 3 April Evening Shift

G1 Physics · Accepted Answer

Use refraction at a spherical surface: μ₂/v - μ₁/u = (μ₂-μ₁)/R. Take positive direction into the glass. μ₁ = 1, μ₂ = 1.5, v = +200 cm, R = +50 cm, and u = -x. Therefore, 1.5/200 - 1/(-x) = (1.5-1)/50. So, 0.0075 + 1/x = 0.01. Hence, 1/x = 0.0025 ⇒ x = 400 cm = 4 m. Thus the magnitude of the source distance is 4 m.