Question

A converging lens of focal length $f_1$ is placed in front of and coaxially with a convex mirror of focal length $f_2$. Their separation is d and whole arrangement is in air. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement.

• A. The diameter of incident and emergent beam is the same
• B. the distance d can be $f_1$
• C. the distance d can be $f_2$
• D. the distance d can be $f_1-2f_2$

Answer 1

Answer: (A), (B), (D)

The correct options are
A the distance d can be $f_1$
B The diameter of incident and emergent beam is the same
D the distance d can be $f_1-2f_2$

There would not be any change in diameter
The image formed by the lens is $v=+f_1$. If this position coincides with the center of the convex mirror, then the ray would retrace back if $d=f-R=f_1-2f_2$
There is another possibility for the ray to retrace back if it hits the mirror at the pole then $d=f_1$
option $A,B,D$ are correct