Question

# A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.

A
12cm behind convex mirror, real
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B
9cm behind convex mirror, real
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C
6cm behind convex mirror, virtual
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D
3cm behind convex mirror, virtual
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Solution

## The correct option is C 6cm behind convex mirror, virtualAccording to given problem, for concave mirror,u=−15 cm and f=−10 cm1v+1−15=1−10, i.e., v=−30 cmi.e., concave mirror will form real, inverted, and enlarged image I1 of object O at a distance of 30 cm from it, i.e., at a distance 40−30=10 cm from the convex mirror.For convex mirror, the image I1 will act as an object and so for it u=−10 cm and f=+15 cm.1v+1−10=115, i.e., v=+6 cmSo, final image I2 is formed at a distance of 6 cm behind the convex mirror and is virtual as shown in figure.

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