Question

A diverging lens of focal length $f_1$ is placed in front of an coaxially with a concave 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. Then, returns as a parallel beam from the arrangement. Then which of the following are correct

• A. The beam diameter of the incident and reflected beams must be the same
• B. $d=2|f_2|-|f_1|$
• C. $d=|f_2|-|f_1|$
• 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
$d=2|f_2|-|f_1|$

The situation for the emergent beam to be parallel again is as shown above. The focus of the diverging lens must be coincident with the center of curvature of the mirror. Thus the parallel incident beam would, after refraction, seem as if diverging from the focus of diverging lens. If this focus is at the center of curvature of the concave mirror, it would retrace the path and would emerge parallel after again refracting from diverging lens.

Since the path is simply retraced, the beam diameter would remain the same.

From the figure, $d=2\left|f_2\right|-\left|f_1\right|$

If immersed in water, the focus of the diverging lens would change.