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

Options

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

Answer

C

Explanation

(1) `n=c/v`
`=(3xx10^ 8)/(2xx10^8)=3/2`
`therefore n=1.5`
(2) From right angle triangle,
`R^2=(R-0.3)^2+(3)^2`
`therefore R^2=R^2-0.6R+0.09+9`
`therefore0.6R=9.09 therefore R=15.15" cm "therefore R=15` cm
(3) From lens maker.s formula,
`1/f=(n-1)((1)/(R_1)-(1)/(R_2))`
`1/f=(1.5-1)((1)/(infty)-(1)/(-15))`
`therefore 1/f=1/2xx(1)/(15)=(1)/(30)" "therefore` f=30 cm