Question:
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 :
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 :
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Apply the lens maker formula to both lenses: \(P=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\), with the plano-convex lens having one flat face.
Updated On: Nov 5, 2026
- \(\dfrac{R}{3}\)
- \(\dfrac{3R}{2}\)
- \(\dfrac{R}{2}\)
- \(2R\)
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The Correct Option is A
Solution and Explanation
Double convex lens: \(R_1=R,\ R_2=-R\), so \(P=(n-1)\left(\dfrac{1}{R}+\dfrac{1}{R}\right)=\dfrac{2(n-1)}{R}\).
Plano-convex lens of the same material: one surface radius \(R^\prime\), the other flat (\(\infty\)), so \(P^\prime=\dfrac{(n-1)}{R^\prime}\).
Given \(P^\prime=1.5P\): \(\dfrac{n-1}{R^\prime}=1.5\times\dfrac{2(n-1)}{R}=\dfrac{3(n-1)}{R}\).
So \(R^\prime=\dfrac{R}{3}\).
Answer: (1) \(\dfrac{R}{3}\)
Plano-convex lens of the same material: one surface radius \(R^\prime\), the other flat (\(\infty\)), so \(P^\prime=\dfrac{(n-1)}{R^\prime}\).
Given \(P^\prime=1.5P\): \(\dfrac{n-1}{R^\prime}=1.5\times\dfrac{2(n-1)}{R}=\dfrac{3(n-1)}{R}\).
So \(R^\prime=\dfrac{R}{3}\).
Answer: (1) \(\dfrac{R}{3}\)
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