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Question

In a convex lens of focal length F, the minimum distance between an object and its real image must be :

A
3F
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B
4F
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C
5F
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D
6F
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Solution

The correct option is B 4F
Let image distance be v, object distance be u and focal length be f.

From lens formula, 1v1u=1f

Let distance between object and image be s,

1v+1u=1f

su(su)=1f

s=u2uf

For point of minima,

dsdu=0

u22uf(uf)2=0

u=0,2f

s=(2f)22ff=4f

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