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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.

1. f' = 2f, f'' = 2f
2. f' = f, f'' = 2f
3. f' = 2f, f'' = f
4. f' = f, f'' = f

Correct answer: f' = 2f, f'' = f

Solution

When the lens is cut along XOX', the focal length of each half remains the same as the original lens (f' = f). When the lens is cut along YOY', the aperture is halved, but the focal length doubles (f'' = 2f). Thus, the correct answer is f' = 2f, f'' = f.

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