Question

A concave mirror of focal length \(f_1\) is placed at a distance \(d\) from a convex lens of focal length \(f_2\). A parallel beam of light coming from infinity parallel to principal axis falls on the convex lens and then after refraction falls on the concave mirror. If it is to retrace the path, the distance \(d\) should be

• A. \( f_1 + f_2 \)
• B. \( -f_1 + f_2 \)
• C. \( 2f_1 + f_2 \)
• D. \( 2f_1 - f_2 \)

Hint:

For retracing of light, rays must strike the mirror normally, i.e., pass through the centre of curvature.

Answer 1

The Correct Option is C

Step 1: Action of the convex lens.
A parallel beam incident on a convex lens converges to its focal point. Thus, the image is formed at a distance \(f_2\) from the lens.
Step 2: Condition for retracing the path.
For the light to retrace its path after reflection, the rays must strike the concave mirror normally. This happens when the image formed by the lens lies at the centre of curvature of the mirror.
Step 3: Using mirror geometry.
The centre of curvature of the concave mirror is at a distance \(2f_1\) from the mirror. Therefore, \[ d = f_2 + 2f_1. \]
Step 4: Conclusion.
The required separation between the lens and the mirror is \( 2f_1 + f_2 \).