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 such that rays reflected from the mirror are parallel after passing through the lens again. If $f=30cm$, then $d$ is equal to

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

Answer 1

Answer: (C)

$45cm$

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, $OD=OE$

$OD+OE=DE$

$⟹OD=DE/2=f/2$

$d=CD+DO=f+f/2=3f/2$

$d=3\times 30/2=45cm$