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Question

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of -

A
20 cm from the plane mirror, it would be a virtual image
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B
20 cm from the lens, it would be a real image
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C
30 cm from the lens, it would be a real image
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D
30 cm from the plane mirror, it would be a virtual image
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Solution

The correct option is A 20 cm from the plane mirror, it would be a virtual image
Using lens formula for first refraction from convex lens,

1v11u=1f

v1=?,u=60 cm,f=30 cm

1v1+160=130v1=60 cm


Here I1 is the first image by the lens.

The plane mirror will produce an image at distance 20 cm to the left of it.

For second refraction from convex lens,

u=20 cm,v=?,f=30 cm

From lens formula,

1v1(20)=130v=60 cm

Thus, the final image is virtual and at a distance, 60 cm40 cm=20 cm from the plane mirror.

Hence, option (A) is the correct answer.

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