A plano-convex lens when silvered on the plane side behaves line a concave mirror of focal length 60 cm. However when silvered on the convex side it behaves like a concave mirror of focal length 20 cm. Then the refractive index of the lens

Options

A. 3
B. 1.5
C. 1
D. 2

Answer

B

Explanation

`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)=(2)/(f_l)+(1)/(infty)=(2)/(f_l)`
`(1)/(60)=(2)/(f_l)`
`(1)/(F')=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)=(2)/(f_l)+(1)/((R)/(2))`
`(1)/(20)=(1)/(60)+(2)/(R)impliesR=60cm`
`(1)/(f_l)=(mu-1)((1)/(R)-(1)/(infty))`
`(1)/(30)=((mu-1))/(60)impliesmu=1.5`