The diameter of a plano convex lens is `6 cm` and thickness at the centre is `3 mm`. If the speed of light in the material of the lens is `2 xx 10^8 m//s`, what is the focal length of the lens ?

Options

A. 20 cm
B. 30 cm
C. 10 cm
D. 15 cm.

Answer

D

Explanation

`D=+6cm = 6xx10^(-2)m`
Thickness at centre = 3mm
`d=3xx10^(-3)m`

`v=2xx10^(8)m//s`
`rArr (R-d)^(2)+((D)/(2))^(2)=R^(2)`
`because " d is very small, "`
`(R-d)^(2)=R^(2)-((D)/(2))^(2)`
`rArr" "R=((6xx10^(-2))^(2))/(8xx3xx10^(-3))`
`rArr" "R=(36xx10^(-4))/(24xx10^(-3))` `rArr" "v=(c)/(""_(a)mu_(g))`
`rArr" "_(a)mu_(g)=(c)/(v)=(3xx10^(8))/(2xx10^(8))=3//2`
From lens maker.s formula
`rArr" "(1)/(f)=(""_(a)mu_(g)-1)[(1)/(R)+(1)/(R)]=((3)/(2)-1)[(2)/(R)]`
`rArr" "(1)/(f)=(1)/(2)xx(2)/(R)=(1)/(R)`
`rArr" "f=R=+15cm`