Question

A concave mirror of focal length 'f1' is placed at a distance of 'd' from a convex lens of focal length 'f2'. a beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. the distance 'd' must equal :-

Answer 1

as you know, image form in focus , when light comes form infinity .
so, parallel beam of light forms image at f₂ , after refraction with convex lens.
Now, image assumed like object for concave mirror, and we know, when object placed at centre of curvature , image form same position .
Hence, it is require that concave mirror should be placed 2× focus of concave mirror from first image.
Hence, distance between convex lens and concave mirror = focal length of convex lens + 2 × focal length of concave mirror = f₂ + 2f₁
Hence, d = 2f₁ + f₂

Answer 2

Answer: -2f1+f2

Explanation:

Light comes from infinity on convex lens so the image is formed at focus of f2 then if we consider there is center of curvature of concave mirror then light will retrace it's path come to focus on convex lens and from there to infinity.

Hope it helps ❤️