# An equiconvex lens is cut into two halves along (i) XOX’ and (ii) YOY’ as shown in the figure. Let f, f ’,f ’’

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An equiconvex lens is cut into two halves along (i) XOX’ and (ii) YOY’ as shown in the figure. Let f, f ’,f ’’ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.

Choose the correct statement from the following :

(A) f ’ = f, f ’’ = f

(B) f ’ = 2f, f ’’ = 2f

(C) f ’ = f, f ’’ = 2f

(D) f ’ = 2f, f ’’ = f

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Correct option: (C) f ’ = f, f ’’ = 2f

Explanation:

Initially, the focal length of equiconvex lens is

Case I :When lens is cut along XOX’ then each half is again equiconvex with

Case II : When lens is cut along YOY’, then each half becomes plano-convex with