A concave mirror of focal length 'f $_{1}$ ' is placed at a distance 'd' from a convex lens of focal length…

A concave mirror of focal length 'f $_{1}$ ' is placed at a distance 'd' from a convex lens of focal length 'f 2 '. A parallel beam of light coming from infinity parallel to principal axis falls on the convex lens and then after refraction falls on the concave mirror. If it is to retrace the path, the distance 'd' should be
  1. $\mathrm{f}_{1}+\mathrm{f}_{2}$
  2. $-\mathrm{f}_{1}+\mathrm{f}_{2}$
  3. $2 \mathrm{f}_{1}+\mathrm{f}_{2}$
  4. $2 \mathrm{f}_{1}-\mathrm{f}_{2}$

Solution

The convex lens will form image at its focus, i.e. at a distance $f_{2}$ from it. If this image falls on the centre of curvature of the concave mirror, the rays falling on it will be normal to the mirror and retrace their path. Hence $d=2 f_{1}+f_{2}$

Asked in: MHT CET 2020 (19 Oct Shift 1)

Practice more Optics questions on Aicharya