A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is :

Solution

Physics sir · 3 steps

Write the lens maker's formula for both lenses; dividing them cancels the (μ - 1) factor.

1. Double convex lens. Both surfaces have radius R, with R₁ = +R and R₂ = -R. The lens maker's formula gives P = (μ - 1)(1/R + 1/R) = 2(μ - 1)/R.
2. Plano-convex lens. Let the curved surface have radius R'. The flat side has infinite radius, so it adds nothing, and the power is (μ - 1)/R'.

   (μ - 1)/R' = 1.5 × 2(μ - 1)/R = 3(μ - 1)/R

3. So. The material is the same, so (μ - 1) cancels and R' = R/3. The answer is (a).

The idea to keep. Same material means the same (μ - 1), so power depends only on the curvature terms. A flat face contributes zero, and a higher power always needs a smaller radius.

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