Q. A double convex lens $\left( R_{1} = \ R_{2} = \ 100\ cm \right)$ having focal length equal to the focal length of a concave mirror. The radius of the concave mirror is

A) 10 cm
B) 20 cm
C) 40 cm
D) 15 cm
Explanation

(b) Focal length of convex lens
$\frac{1}{f} = (\mu - 1)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
$R_{1}\ = \ 10\ cm,\ R_{2} = - 10\ cm,\ \mu\ = \ 1.5$ (for glass)
$\frac{1}{f} = (1.5 - 1)\left( \frac{1}{10} - \frac{1}{- 10} \right)$
$\ \ \ \ = \ 0.5\left( \frac{2}{10} \right)$
$f = \frac{10}{2 \times 0.5}$
$\Rightarrow f\ = \ 10\ cm$
$\therefore$ Focal length of concave mirror
= 10 cm
$\therefore$ Radius of curvature $= \ 2 \times 10\ = \ 20\ cm$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.