Question

A plano-convex lens of focal length 30 cm has its plane surface silvered. An object is placed 40 cm from the lens on the convex side. The distance of the image from the lens is :

• A. 18 cm
• B. 24 cm
• C. 30 cm
• D. 40 cm

Answer 1

The correct option is B 24 cm

The focal length of combination of lens and one its back surface silvered for it to be act as a mirror is given by:-

$\frac{1}{f}=\frac{-2}{f_l}+\frac{1}{f_m}$

where $f_l$=focal length of lens

and $f_m$=focal length of mirror formed

Here, $f_l=30cm$ and for plane mirror $f_m=\infty$

$⟹\frac{1}{f}=\frac{-2}{30}+\frac{1}{\infty }$

$⟹f=-15cm$

Now, for mirror:-

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

$⟹\frac{1}{v}=\frac{-1}{15}-\frac{1}{-40}=\frac{-1}{15}+\frac{1}{40}$

$v=-24cm$

Answer-(B)