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

A. At the object position — The lens forms an image at 60 cm behind it. This image acts as an object for the mirror at 30 cm, which reflects it back to the same position, and the lens then forms the final image at the original object location.

JEE Main · PhysicsHard

$A concave mirror of focal length $f_m = -10 \text{ cm}$ is placed at a distance of $d = 30 \text{ cm}$ from a convex lens of focal length $f_l = 15 \text{ cm}$. An object is placed $u = -20 \text{ cm}$ in front of the lens. Find the position of the final image.$

A.At the object position
B.At infinity
C. $10 \text{ cm}$
D. $20 \text{ cm}$

Show correct answer & step-by-step solution

Correct answer: A — At the object position

Solution

Lens formula:

1/ v - 1/ (- 20) = 1/15 ⟹ v = 60 cm

. Mirror object distance

u_{m} = - (60 - 30) = - 30 cm

. Mirror image

v_{m} = - 15 cm

. Final lens refraction results in image at

u = - 20 cm

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