Radii of curvature of a converging lens are in the ratio `1 : 2`. Its focal length is 6cm and refractive index is 1.5. Then its radii of curvture are _____ respectively.

Options

A. 9 cm and 18 cm
B. 6cma nd 12 cm
C. 3 cm and 6cm
D. 4.5 cm and 9 cm

Answer

D

Explanation

Let `R_(1) = R :. R_(2) = 2R`
According to lens maker's formula
`(1)/(f) = (mu -1) ((1)/(R_(1)) - (1)/(R_(2)))`
Here, `f= 6cm, mu = 1.5`
`R_(1) = R, R_(2) = -2R`
`:. (1)/(6) = (1.5 -1) ((1)/(R ) - (1)/(-2R)) = 0.5 ((1)/(R )+ (1)/(2R))`
`(1)/(6) = 0.5 ((3)/(2R)) or (1)/(6)= (1.5)/(2R)`
`R+ (1.5 xx 6)/(2) = 4.5cm`
`:. R_(1) = 4.5 cm, R_(2) = 9cm`