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Question

# A lens of focal length f produces an image of an object located 15 cm on one side of it at a distance of 30 cm on the other side. If the lens is replaced by another lens of focal length f2, where would the image form? If the image has to form at the earlier position by what distance should the object be shifted?

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Solution

## Here object distance u=−15 cm v=30 cmSo, using the lens' formula1f=1v−1u1f=130−1−15f=10 cmWhen the focal become half f1=f/2=5 cmLet say image forms at v1So 1f1=1v1−1u15=1v1−1−15v1=7.5 cmIf the image has to form at the earlier position,Let say object is placed at u1v=30 cm 1f1=1v−1u115=130−1u1u1=−6 cmSo initially it was at 15 cm and now it should be placed at 6 cm from lens.So it need to move 15−6=9 cm towards lens.

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