A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30 cm. However, when silvered on the convex side it behaves like concave mirror of focal length 10 cm. Then the refractive index of its material will be:

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` .