Question

Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature, what is the radius of curvature required if the focal length is to be 20 cm?

Answer 1

focal length of convex lens , f = 20cm

refraction index of lens made by glass , $\mu$ =1.55

use formula, $\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

a/c to question, both the faces of lens are of same radius radius .
e.g., $R_1=R$ and $R_2=-R$

so, $\frac{1}{f}=(\mu-1)\left(\frac{1}{R}+\frac{1}{R}\right)$

or, 1/20 = (1.55 - 1)(2/R)

or, 1/20 = 0.55 × 2/R

or, 1/20 = 1.1/R

or, R = 20 × 1.1 = 22 cm

hence, radius of curvature of lens = 22cm