A concave mirror of focal length 6 cm is placed at a distance ‘d’ from the convex lens of focal length 8 cm. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance ‘d’ must be equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 cm
Rays from infinity are parallel, so the lens focuses them at its focal point, 8 cm behind the lens. This image is the object for the mirror. For the light to return to infinity it must retrace its path and leave the lens as a parallel beam. That happens when the rays strike the mirror normally, which is the case when the image formed by the lens lies at the centre of curvature of the mirror, at a distance \( 2f_{m} \) from it.
\( d = f_{\text{lens}} + 2f_{\text{mirror}} = 8\,\mathrm{cm} + 2\times6\,\mathrm{cm} = 20\,\mathrm{cm} \)