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Question

# A convex lens has its radii of curvature equal. The focal length of the lens is f. If it is divided vertically into two identical plano-convex lenses by cutting it, then the focal length of the plano-convex lens is:[μ− the refractive index of the material of the lens]

A
f
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B
f2
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C
2f
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D
(μ1)f
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Solution

## The correct option is C 2fUsing lens-maker formula : 1f=(μ−1)(1R1−1R2)For convex lens : R1=R R2=−R∴ 1f=(μ−1)(1R−1−R) ⟹ 1f=(μ−1)2R ........(1)For plano-convex lens : R1=R R2=∞∴ 1f′=(μ−1)(1R−1∞) ⟹ 1f′=(μ−1)1R=12f ⟹ f′=2f Thus the focal length of Plano-convex lens is 2f.

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