A concave mirrorr 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 mirrorr combination returns to infinity. The distance `d` must equal.

Options

A. `f_(1) + f_(2)`
B. `-f_(1) + f_(2)`
C. `2f_(1) + f_(2)`
D. `-2 f_(1) + f_(2)`

Answer

C

Explanation

In Fig.

focal length of concave mirror `= f_(1)` and focal length of convex lens `= f_(2)`.
A beam of light coming from infinity and falling on convex lens, converges at focus `O` of convex lens. Therefore, `C_(1)O = f_(2)`. The rays of light from `O` will retrace their path on reflection from concave mirror only when, i.e., `OP = R = 2 f_(1)`.
`:. C_(1)P = d = C_(1)O + OP = (f_(2) + 2 f_(1))`