A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of convex mirror ?

Explanation

Given : `-u=0.12m`
`x=0.10m, f=0.10m`
using the formula `(1)/(f)=(1)/(-u)+(1)/(v)` we write
`(1)/(0.10)=(1)/(0.12)+(1)/(v)`
`therefore (1)/(v)=(10)/(1)-(100)/(12)=(120-100)/(12)=(20)/(12)`
`therefore v=(12)/(20)=(3)/(5)=0.60m`
From the fig., radius of curvature of the mirror is `0.60-0.10=0.50`m so that the focal length of the convex mirror `f=(r)/(2)=(0.50)/(2)=0.25m`.