A 5 cm long needle lies along the principal axis axis of a concave miror of focal length 20 cm in such a way that the end closer to the pole is 40 cm from it.Find the length of the image of the needle formed by the mirror.

Explanation

Position of nearer end of the needle:
`u_(1) =-40 cm`
`f =-20 cm`
`v_(1)`= ?
`1/u_(1) + 1/v_(1) = 1/f`
`1/v_(1) = 1/f -1/u_(1) =-1/20 -1/(-40)`
`=-1/20 + 1/40`
`1/v_(1) =(-2+1)/40 =-1/40`
`v_(1) =- 40 cm`
Position of the farther, end of the needle
`u_(2) =-(40 + 5) = -45 cm`
`f =-20 cm`
`1/u_(2) + 1/v_(2) = 1/f`
`-1/45 + 1/v_(2) =-1/20`
`-5/80 =-1/36`
`v_(2) =-36 cm`
`therefore` Length of image of.the needle
`=-36 -(-40)= 4 cm`