A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length `28 cm` . When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concave mirror of focal length `10 cm` then the refractive index of the mateiral of the lens is:

Options

A. `9//14`
B. `14//9`
C. `17//9`
D. NONE

Answer

C

Explanation

Focal length of plano-convex lens is `10cm` .
`(1)/(10)=((3)/(2)-1)((1)/(infty)-(1)/(-R))`
(1)/(10)=(1)/(2)xx(1)/(R) implies R=5 cm`
Let focal length of water lens is `f_(w)`
`(1)/(f_(w))=((4)/(3)-1)((1)/(-5)-(1)/(5))`
(1)/(f_(w))=(1)/(3)xx(-(2)/(5))=(-2)/(15)`
Optical power of system
`P=(1)/(f)+(1)/(f)+(1)/(f_(w))`
`=(1)/(0.1)+(1)/(0.1)+(-(40)/(3))`
`=6.67 D` .