An object is placed 30 cm in front of a convex mirror of focal length 30 cm. A plane mirror is placed between the object and convex mirror so that the images formed by the two mirrors coincide. The distance between the two mirrors is:
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Question

An object is placed 30 cm in front of a convex mirror of focal length 30 cm. A plane mirror is placed between the object and convex mirror so that the images formed by the two mirrors coincide. The distance between the two mirrors is:

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G1 Physics · Accepted Answer

First find the image formed by the convex mirror. Using the mirror formula with u = -30 cm, f = +30 cm: 1/f = 1/v + 1/u ⇒ 1/30 = 1/v - 1/30 ⇒ 1/v = 2/30 ⇒ v = +15 cm. So the convex mirror forms a virtual image 15 cm behind it. Let the plane mirror be x cm in front of the convex mirror. The object is then (30-x) cm in front of the plane mirror. A plane mirror forms its image the same distance behind itself. Measured from the convex mirror, the plane-mirror image lies at (30-x)-x = 30-2x cm behin…