JEE Main 2022 · 27 June · evening · Single correct · +4 / −1
A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.
- (a) Power of L₁ = P/2
- (b) Power of L₂ = P/2
- (c) Power of L₃ = P/2
- (d) Power of L₁ = P
Answer and solution
Answer (a) Power of L₁ = P/2
Solution
Physics sir · 2 steps
Power depends on the curved surfaces a piece keeps, not on how much glass it keeps.
- What sets power. By the lens maker's formula, P = (μ - 1)(1/R₁ - 1/R₂). Only the refractive index and the radii of the two surfaces matter. The size of the lens does not.
P = (μ - 1)2/R ⇒ (μ - 1)1/R = P/2
Piece Made by Surfaces left Power L₁ cut along the principal axis both convex surfaces, radius R each P L₂ upper half cut perpendicular to the axis one convex surface and one flat surface P/2 L₃ upper half cut perpendicular to the axis one flat surface and one convex surface P/2 - So. L₁ keeps both curved surfaces, so its power is still P, and L₂ and L₃ are plano-convex with P/2 each. The incorrect statement is (a).
The idea to keep. A cut along the principal axis only reduces the aperture, so the power stays the same. A cut perpendicular to the axis removes one curved surface, so each piece gets its own share of the power.
Answer from the NTA final answer key. Solution by PrepWiser.