A symmetric thin biconvex lens is cut into four equal parts by two planes A B and C D as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

Solution

Physics sir · 4 steps

Power lives in the curved surfaces, not in the size of the glass: track only which surfaces each piece keeps.

1. Lens maker's formula. For the original symmetric lens, both faces have radius R. That gives P = (μ - 1)(1/R + 1/R) = 2(μ - 1)/R = 4 D, so (μ - 1)/R = 2 D.
2. Cut along AB. AB runs along the principal axis and slices the lens into a top half and a bottom half. Each half still has two convex faces of radius R. Only the aperture shrinks, so the power stays 4 D.
3. Cut along CD. CD lies in the plane of the lens and splits it into a left piece and a right piece. Each piece now has one curved face of radius R and one flat face, with R = ∞. It is a plano-convex lens.

   Pₚₐᵣₜ = (μ - 1)(1/R - 1/∞) = (μ - 1)/R = 2 D

4. So. Each quarter is a plano-convex piece with power 2 D, which is option (a).

The idea to keep. Cutting a lens along its axis changes only the aperture, so power stays the same. Cutting it through its plane removes a curved face, and that halves the power of a symmetric lens.

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