Question

A real image of an object is formed at a distance of 20cm from a lens. On putting another lens in contact with it, the image is shifted 10cm towards the combination. The power of the lens is

A
2D
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B
5D
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C
6D
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D
10D
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Solution

The correct option is B 5DAs image formed is real, therefore lens must be convex, v=20cm.Let f1, be the focal length for this lens and f2 be the focal length of the other lens put in contact later.for the first lens, ∴1f1=1v1−1u1=120−1u1-----------------(1)After placing it in contact with another lens, the image shifted to 10cm towards the combinationi.e., v2=(20−10) cm=10 cmLet fnet be the effective focal length of the combination, which can be given as:∴1fnet=1f1+1f2=1v2−1u2=110−1u1⇒1f1+1f2=1v2−1u2=110−1u1--------------(2)From equation (1) and (2):110−1u=1f1+1f2=[120−1u]+1f2⇒110−1u=120−1u+1f2⇒110=120+1f2⇒110−120=1f2⇒1f2=120Hence, f2=20cm∴P=10020m−1=5DSo, the correct option is (B)

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