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

The radius of curvature of one face of the lens=R1
The radius of curvature of the other face of the lens=R2
The radius of curvature of the double-convex lens=R
∴R1=R and R2=-R
The value of R can be calculated as:

$\frac{1}{f}=(\mu-1)[\frac{1}{R_1}-\frac{1}{R_2}]$=$\frac{1}{20}$=(1.55-1)$[\frac{1}{R_1}-\frac{1}{R_2}]$=$\frac{1}{20}$=0.55×$\frac{2}{R}$ ∴R=0.55×2×20=22cm
Hence, the radius of curvature of the double-convex lens is 22cm.