Question

A concave mirror of focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2$. A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity. The distance d must equal

• A. $f_1$ + $f_2$
• B. ${-f}_1$ + $f_2$
• C. ${2f}_1$ + $f_2$
• D. ${-2f}_1$ + $f_2$

Answer 1

The correct option is C ${2f}_1$ + $f_2$

Given: A concave mirror of focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2$. A beam of light coming from infinity and falling on this convex lens, concave mirror combination returns to infinity.

To find the distance $d$

Solution:

The image form at the focus , when light comes from infinity .

In order to form image at infinity after reflection form the concave mirror, this image formed must be at least at the center of the curvature of the concave mirror, so the image is formed at the same point after reflection from the concave mirror and the final image will be formed at infinity after reflection.

Hence, it is require that concave mirror should be placed 2$\times$ focus of concave mirror from first image.

Hence, distance between convex lens and concave mirror = focal length of convex lens + 2 $\times$ focal length of concave mirror

$⟹d=f_2+2f_1$

is the value of $d$