The radii of curvatureof double convex lens of glass `(mu = 1.5)` are in the ratio of `1 : 2`. This lens renders the rays parallel coming from an illuminated filament at a distance of `6 cm`. Calculate the radii of curvature of its surfaces.

Answer

`4.5 cm ; -9.0 cm`

Explanation

Here, `mu = 1.5, Let R_1 = R, R_2 = -2 R`
As rays are rendered parallel, `6 cm` must be the focal length of the lens, i.e., `f = 6 cm`
From `(1)/(f)= (mu - ) ((1)/(R_1) - (1)/(R_2))`
`(1)/(6)=(1.5 - 1) ((1)/( R) + (1)/(2 R)) = (1)/(2) xx (3)/(2 R)`
`R = (18)/(4) = 4.5 cm`
Hence, `R_1 = 4.5 cm, R_2 = -9.0 cm`.