A convex mirror of focal length F1 is placed at a distance d from a convex lens of focal length F2. A beam of light rays coming from infinity falling on convex lens-convex mirror combination and returns back to infinity. Distance d is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (F2 - 2F1)
Light retraces its path after reflection only if it falls on the mirror normally, that is, if it is directed towards the centre of curvature of the mirror.
The convex lens converges the parallel beam towards its focus, at a distance \( F_2 \) behind the lens. This point must be the centre of curvature of the convex mirror, which lies behind the mirror at a distance
\( \displaystyle R = 2F_1 \)
The mirror is in front of that point, so the distance from the lens to the point is
\( \displaystyle d + 2F_1 = F_2 \;\Rightarrow\; d = F_2 - 2F_1 \)
The reflected rays go back along the same paths, through the lens, and leave parallel again towards infinity.