Question

A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed 40 cm apart facing each other’s reflecting surface. A point object is placed between the mirror on their common axis and 15 cm from the concave mirror. Find the position of images produced by reflection at concave mirror first and then at convex mirror.

A
10 cm behind the convex mirror
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B
6 cm behind the convex mirror
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C
10 cm infront of the convex mirror
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D
6 cm infront of the convex mirror
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Solution

The correct option is B 6 cm behind the convex mirror For mirror M1, O act as an object. Let its image be I1. Then u=−15 cm,f=−10 cm ⇒1v−115=1−10⇒v=−30 cm Image I1 will act as an object for mirror M2 its distance from mirror M2 u1=−(40−30) cm=−10 cm So 1v1+1u1=1f⇒1v1+1−10=115⇒v1=+6 cm Therefore, image I2 is formed at a distance 6 cm behind the convex mirror and is virtual.

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