Diameter of a plano-convex lens is 6cm and thickness at the centre is 3mm. If speed of light in material of lens is `2xx10^(8)(m)/(s)`, The focal length of the lens is

Options

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

Answer

C

Explanation

`2y=6cm` i.e., `y=3cm`
`t=3mm=0.3cm`
In `triangleAOC`
`R^2=y^2+(R-t)^2`
`R^2=y^2+R^2-2Rt+t^2`
Since `t` is small `t^2` is negligible
`R=(y^2)/(2t)=(3xx3)/(2xx0.3)=15cm`
`mu=(c)/(v)=(3xx10^8)/(2xx10^8)=(3)/(2)`
`(1)/(f)=(mu-1)((1)/(R)-(1)/(infty))=((3)/(2)-1)((1)/(15))=(1)/(30)`
`f=30cm`