JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Geometrical Optics

Given is a thin convex lens of glass (refractive index

μ

) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.

(A) $R / μ$
(B) $R / (2 μ - 3)$
(C) $μ R$
(D) $R / (2 μ - 1)$ ✓ Correct

Answer: (D)

Solution

Light entering through the unsilvered curved face refracts, travels through the glass, reflects off the silvered curved face acting as a mirror, and refracts again on the way out through the same unsilvered face. The system behaves as an equivalent mirror whose power is

P_{e q} = 2 P_{r e f r a c t i o n} + P_{mi r r or},

since the refracting surface is used twice.

Power of the single refracting surface (radius

R

, index

μ

P_{r e f r a c t i o n} = \frac{μ - 1}{R} .

Power of the silvered surface acting as a mirror inside the medium of index

μ

P_{mi r r or} = \frac{2 μ}{R} .

P_{e q} = \frac{2 ( μ - 1 )}{R} + \frac{2 μ}{R} = \frac{4 μ - 2}{R} = \frac{2 ( 2 μ - 1 )}{R} .

The equivalent focal length is

F_{e q} = \frac{R}{2 ( 2 μ - 1 )}

. For the final image to coincide with the object, the object must sit at the centre of curvature of this equivalent mirror, i.e. at a distance

u = 2 F_{e q} = \frac{R}{2 μ - 1} .

JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Geometrical Optics →

JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Geometrical Optics

Solution

More JEE Main questions on Geometrical Optics