A concave mirror of focal length f_1 is place | vedclass

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Question

(B) For a beam of light coming from infinity to return to infinity after passing through the lens and reflecting from the mirror,the rays must strike

Vedclass · Accepted Answer

$2f_1 + f_2$

Vedclass · Answer

(B) For a beam of light coming from infinity to return to infinity after passing through the lens and reflecting from the mirror,the rays must strike the concave mirror normally.This happens if the rays incident on the mirror appear to be coming from its center of curvature.The convex lens focuses the parallel beam of light at its focal point,which is at a distance $f_2$ from the lens.For the rays to strike the concave mirror normally,this focal point must coincide with the center of curvature of the concave mirror.The distance of the center of curvature from the concave mirror is $2f_1$.Therefore,the total distance $d$ between the lens and the mirror is the sum of the focal length of the lens and the radius of curvature of the mirror:$d = f_2 + 2f_1$.

$A$ 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:

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