Question

A concave mirror of focal length ′f′1 is placeed 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 dsitance '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