A plano-convex lens when silvered on the plane side behaves like 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. `3.0`
B. `1.5`
C. `1.0`
D. `2.0`

Answer

B

Explanation

`(1)/(F)=(1)/(f_(1))+(1)/(f_(1))+(1)/(f_(m))`
`(1)/(F)=(2)/(f_(1))+(1)/(f_(m))`
or `(1)/(F)=2(mu-1)((1)/(R))+(1)/(oo)`
or`F=(R)/(2mu(-1))`
Now, `-60=(-R)/(2(mu-1))`
or `120(mu-1)=R`
Again`(1)/(F)=(1)/(f_(1))+(1)/(f_(1))+(1)/(f_(m))`
or`(1)/(F)=(2)/(f_(1))+(1)/(R//2)`
or` (1)/(F)2(mu-1)((1)/(R))+(2)/(R)`
or `(1)/(F)=(2)/(F)(mu-1+1)`
or `F=(R)/(2mu)`
Now, `-20=(-R)/(2gmu)` or `40mu=R`
Dividing (1) and (2) , we get
`(120(mu-1))/(40mu)=(R)/(R)=1`
or `120(mu-1)=40mu`
or `120mu-40mu=120`
or `80mu=120`
or `mu=(120)/(80)=(3)/(2)=1.5`