JEE Main 2025 · 7 April · morning · Single correct · +4 / −1

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

  1. (a) 5 D
  2. (b) 1 D
  3. (c) 20 D
  4. (d) 10 D
Answer and solution

Answer (d) 10 D

Solution

Physics sir · 3 steps

Lenses with a gap between them: subtract the separation term before you add the powers.

  1. Separated lenses. When two thin lenses are a distance d apart, the sum of their powers is not the full story. There is an extra term for the gap.

    1/F = 1/f₁ + 1/f₂ - d/(f₁ f₂)

  2. Put in numbers. With f₁ = 30 cm, f₂ = 10 cm and d = 10 cm: 1/F = 1/30 + 3/30 - 10/300 = 1/30 + 3/30 - 1/30 = 3/30 = 1/10 cm⁻¹. So F = 10 cm = 0.1 m.
  3. So. P = 1/F = 1/(0.1 m) = 10 D, which is option (d).

The idea to keep. Powers add directly only when the lenses touch. If there is a gap d, use P = P₁ + P₂ - dP₁P₂, and put focal lengths in metres before writing power in dioptres.

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

Study Ray Optics

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