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Question

A convex lens of focal length 40cm is held at a distance 12cm coaxially above a concave mirror of focal length 18cm. If the convex lens is replaced by a concave lens of focal length 60cm, it gives rise to an image coincident with itself. Then the object distance d is :

161213_7ed0900a970b40aca476215f186e1fce.png

A
20cm
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B
30cm
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C
40cm
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D
60cm
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Solution

The correct option is C 40cm
The ray originating from point O at first gets refracted from the concave lens of focal length 60 cm and forms an image at point I1

Using lens formula, 1v1u=1f2

Given: u=d f2=60cm

1v1d=160

v=60dd+60

Now the image formed will act as source for the concave mirror, and if the final image is formed at point O, then the ray form point I1 has to trace the same path after reflection from the mirror i-e, the ray from I1 must fall normally on the mirror.Thus I1 should be at the radius of curvature

R of the mirror.

R=2f1=36cm

Hence 1260dd+60=36

d=40cm

411236_161216_ans_13b8546aa53348cc878fb14f9a070747.png

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