Q. The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is

A) Greater than zero but less than 1.5
B) Greater than 1.5 but less than 2.0
C) Greater than 2.0 but less than 2.5
D) Greater than 2.5 but less than 2.0
Explanation

(a) Focal length of lens
$\frac{1}{f} = (\mu - 1)(\frac{1}{R_{1}} - \frac{1}{R_{2}})$
For equi-convex lens,
$R_{1} = + R,\ R_{2} = \ - R$
$\therefore\ \frac{1}{f} = \ (\mu - 1)\left( \frac{1}{R} - \frac{1}{- R} \right)$
$\frac{1}{f} = (\mu - 1)\left( \frac{2}{R} \right)$
$f = \frac{R}{2(\mu - 1)}$
$f < R,\ so,\ 2(\mu - 1) < 1$
$(\mu - 1) < \frac{1}{2}$
$(\mu - 1) < 0.5$
$\mu < 1.5$
Focal length of convex lens is positive. So, $\mu\ $cannot be negative, hence should be greater than zero but less than 1.5

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

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