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 $d$. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement.

• A. The beam diameter of the incident and reflected beams must be the same
• B. $d=f_1-2\left|f_2\right|$
• C. $d=f_1-\left|f_2\right|$
• D. If the entire arrangement is immersed in water, the conditions will remain unaltered

Answer 1

Answer: (A), (B)

The beam diameter of the incident and reflected beams must be the same
$d=f_1-2\left|f_2\right|$

Since the beam of light retraces the path, the beam diameter of incident and reflected beams must be same.

Also to retrace the path, the light refracted from the converging lens must fall on the center of curvature of the convex mirror.

Thus $f_1=d+2\left|f_2\right|$

$⟹d=f_1-2\left|f_2\right|$