Question

A point source of light is placed at 2f from a converging lens of focal length f. A flat mirror is placed on the other side of the lens at a distance d from lens such that rays reflected from the mirror are parallel after passing through the lens again. If f=30 cm, then d is equal to

• A. 15 cm
• B. 30 cm
• C. 45 cm
• D. 75 cm

Answer 1

The correct option is C 45 cm

For object placed at center of curvature of lens, image is formed at center of curvature on other side of the lens.
Hence, CE=2f
Since, final refracted rays are parallel to the axis, rays are coming from focus of the lens
CD=f
DE=CE-CD=2f-f=f
Using laws of reflection, OD=OE
OD+OE=DE
$\Rightarrow$ OD=DE/2=f/2
d=CD+DO=f+f/2 =3f/2
d=3x30/2=45 cm