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Question

A concave mirror of focal length 10 cm and an 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
12 cm behind convex mirror, real
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B
9 cm behind convex mirror, real
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C
6 cm behind convex mirror, virtual
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D
3 cm behind convex mirror, virtual
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Solution

The correct option is C 6 cm behind convex mirror, virtual
According to given problem, for concave mirror.
u=15 cm and
f=10 cm
1v+115=110
v=30 cm

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 4030=10 cm from the convex mirror.

For convex mirror, the image I1 will act as an object
u=10 cm and
f=+15 cm
1v+110=115
v=+6 cm

So, final image I2 is formed at a distance of 6 cm behind the convex mirror and is virtual.
Why this question?

Tip: When you have more than one mirror, you can create multiple reflections. These multiple reflections can lead to multiple images. Each image acts as object for next reflection.

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