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Question

# A plane mirror is placed at a distance of 50 cm from a concave mirror of focal length 16 cm. Where should a short object be placed between the mirrors and facing both the mirrors so that its virtual image in the plane mirror coincides with the real image in concave mirror?

A
10 cm from the plane mirror
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B
20 cm from the plane mirror
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C
30 cm from the plane mirror
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D
It is not possible for the images to coincide
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Solution

## The correct option is C 30 cm from the plane mirror Let the object be at a distance x from the plane mirror. The distance of object from concave mirror =50−x For the plane mirror, object and image distances are equal. A′M=AM=x ⇒OA′=OM+A′M=50+x For the concave mirror image distance is 50+x Using sign convention u=−(50−x),v=−(50+x),f=−16 cm From mirror formula, 150−x+150+x=116 ⇒100502−x2=116⇒x=30 cm The object must be placed at a distance of 30 cm from the plane mirror. Why this Question? Caution: Not to confuse with case of multiple reflection. In this question we are finding image of an object using both plane mirror and concave mirror.

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