JEE Main 2025 · 24 January · morning · Single correct · +4 / −1

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m . The radius of curvature of the curved surface of the lens is

  1. (a) 0.15 m
  2. (b) 0.10 m
  3. (c) 0.25 m
  4. (d) 0.20 m
Answer and solution

Answer (b) 0.10 m

Solution

Physics sir · 3 steps

Light crosses the lens twice and bounces off a plane mirror once, so add the powers: P = 2P_L.

  1. Path of light. Light enters through the curved face and refracts through the lens. It reflects off the silvered plane face, then refracts through the lens again on the way out. So the system power is P = 2P_L + P_M, and a plane mirror has P_M = 0.
  2. Lens in liquid. In the liquid, the lens maker's formula uses the relative index 1.5/1.2 = 1.25. The plane face has R = ∞, so 1/f_L = (1.25 - 1)1/R = 0.25/R.

    1/F = 2/f_L = (2 × 0.25)/R = 0.5/R ⇒ F = 2R

  3. So. With F = 0.2 m, 2R = 0.2 m, so R = 0.10 m. That is option (b).

The idea to keep. For any silvered lens, add the powers: the lens counts twice and the mirror once. A lens in a liquid always uses μₗₑₙₛ/μ_(liquid) in the lens maker's formula.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 200 times in JEE Main since 2020. This question is from 2025.