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 20cm?

Explanation

Here, focal length of convex lens f = + 20 cm
Refractive index of glass `mu = 1.55`
Suppose `R_1 = R` and `R_2 =-R`
From lens maker.s formula,
`1/f (mu-1) [1/R_1 - 1/R_2]`
`1/20 = (1. 55 - 1. 00) [ 1/R + 1/R]`
`1/ 20 = (0.55 xx 2)/(R)`
`therefore R =1 . 1 xx 20 = 22 cm `