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Question

Where should a convex lens of focal length 9 cm be placed (in cm) between two point sources S1 and S2 which are 24 cm apart, so that images of both the sources are formed at the same place? Find distance of lens from S1 or S2 whichever is lesser.

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Solution

Let the distance from the lens to the first source be x. Then distance from lens to second source is 24x

Applying lens formula for S2,

1v1u=1f
1v=19124x

For S1,

1v1u=1f
1v+1x=19
1v=191x

Equating the two,

19124x=191x
x224x+108=0
i.e x=6 or 18

The lesser value is x=6.

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