Question

The convex lens of a thin plano-convex lens `(mu=1.5)` with `R=60cm` is silvered to obtain a concave mirror. An object is located at a distance 25 cm in front of this mirror, find the distance of the image from mirror.

Answer 1

`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)=(2)/(f_l)+(1)/(f_m)`
`=2(mu-1)((1)/(infty)-(1)/(-R))+(1)/((R)/(2))`
`=2((3)/(2)-1)((1)/(60))+(2)/(60)=(1)/(60)+(2)/(60)=(1)/(20)`
The silvered lens will behave as concave mirror of focal length 20 cm
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/(-25)=(1)/(-20)`
`(1)/(v)=-(1)/(20)+(1)/(25)=(-5+4)/(100)`
`v=-100cm`
Distance of image from mirror `=100cm`