Ray Optics

JEE Main level, single correct, medium

185 of 295

Question 185 of 295

A double convex lens has power PP and same radii of curvature rr of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5P1.5P is :

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Answer: (D) R3\dfrac{R}{3}

1P=(n−1)(1R−1−R)\dfrac{1}{P}=(n-1)\left(\dfrac{1}{R}-\dfrac{1}{-R}\right)
1P=(n−1)2R\dfrac{1}{P}=(n-1)\dfrac{2}{R} .........(1)\left(1\right)
11.5P=(n−1)(1R−1∞)\dfrac{1}{1.5P}=(n-1)\left(\dfrac{1}{R}-\dfrac{1}{\infty }\right) .......(ii)\left(ii\right)
23P=n−1R\dfrac{2}{3P}=\dfrac{n-1}{R}
From (i)\left(i\right) and (ii)\left(ii\right)
32=R′2R\dfrac{3}{2}=\dfrac{{R}^{'}}{2R}
⇒\Rightarrow R′=R3{R}^{'}=\dfrac{R}{3}

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