Concept: For a combination of optical elements to return a parallel beam back to infinity, the net focal length must be infinite, meaning the focal point is at infinity.
Explanation:1. A beam of light from infinity falling on the convex lens will converge at its focal point, which is at a distance
f2 from the lens.
2. The concave mirror is placed at a distance
d from the lens. For the light to return to infinity after reflection from the mirror, the light rays must be incident on the mirror normally. This means the rays must be directed towards the center of curvature of the mirror.
3. Therefore, the focal point of the convex lens must coincide with the center of curvature of the concave mirror.
4. The center of curvature of a concave mirror is at a distance
2f1 from the mirror.
5. The distance between the lens and the mirror is
d. The distance of the image formed by the lens from the mirror is
(f2−d).
6. For normal incidence on the mirror, this image must be at the center of curvature of the mirror. So,
(f2−d)=−2f1 (since the image is formed on the same side as the object for the mirror, and the center of curvature is on the left of the mirror).
7. Rearranging the equation:
d=f2+2f1.
Answer: 2f1+f2
