Question

A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5 :

• A. 100 cm, 50 cm
• B. 25 cm, 50 cm
• C. 18.75 cm, 37.5 cm
• D. 50 cm, 100 cm

Answer 1

Answer: (C)

$\frac{1}{f}=\left(\frac{{\mu }_2-{\mu }_1}{{\mu }_1}\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$\Rightarrow \frac{1}{25}=\left(\frac{1.5-1}{1}\right)\left(\frac{1}{R}-\frac{1}{\left(-2R\right)}\right)$
$\Rightarrow \frac{2}{25}=\frac{3}{2R}$
$\Rightarrow R=\frac{75}{4}=18.75$