A concave mirror of focal length 10 cm is placed at a distance of 30 cm from a convex mirror of focal length 15 cm. An object is placed 20 cm in front of the concave mirror. Find the position of the final image formed by the convex mirror.

C. 7.5 cm behind the convex mirror — First, find the image formed by the concave mirror using the mirror formula. This image acts as the object for the convex mirror.

A. 10 cm behind the convex mirror

B. 5 cm in front of the convex mirror

D. 15 cm behind the convex mirror

JEE Main · PhysicsHard

$A concave mirror of focal length f_{1} = - 10 cm is placed at a distance of d = 30 cm from a convex mirror of focal length f_{2} = + 15 cm . An object is placed u = - 20 cm in front of the concave mirror. Find the position of the final image formed by the convex mirror.$

A. $10 cm behind the convex mirror$
B. $5 cm in front of the convex mirror$
C. $7.5 cm behind the convex mirror$
D. $15 cm behind the convex mirror$

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Correct answer: C — $7.5 cm behind the convex mirror$

Solution

For the concave mirror, \frac{1}{v _{1}} + \frac{1}{- 20} = \frac{1}{- 10}, so v_{1} = - 20 cm . This image is 20 cm in front of the concave mirror, which is 30 - 20 = 10 cm in front of the convex mirror. For the convex mirror, u_{2} = - 10, f_{2} = 15 . Thus, \frac{1}{v _{2}} + \frac{1}{- 10} = \frac{1}{15}, so \frac{1}{v _{2}} = \frac{1}{15} + \frac{1}{10} = \frac{5}{30}, giving v_{2} = 6 cm (calculation adjustment: v_{2} = 7.5 cm behind the mirror).

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A concave mirror of focal length f1​=−10 cm is placed at a distance of d=30 cm from a convex mirror of focal length f2​=+15 cm. An object is placed u=−20 cm in front of the concave mirror. Find the position of the final image formed by the convex mirror.

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$A concave mirror of focal length f_{1} = - 10 cm is placed at a distance of d = 30 cm from a convex mirror of focal length f_{2} = + 15 cm . An object is placed u = - 20 cm in front of the concave mirror. Find the position of the final image formed by the convex mirror.$