A short object of length `L` is placed along the principal axis of a concave mirror away from focus. The object distance is `u`. If the mirror has a focal length `f`, what will be the length of the image ? You may take `L lt lt | u - f |`.

Explanation

Mirror formula can be written as follows :
`(1)/(v)+(1)/(u)=(1)/(f) rArr v=(uf)/(u-f)`
`rArr" "(dv)/(du)=((u-f)(f)-uf(1-0))/((u-f)^(2))`
`rArr" "(dv)/(du)=-(f^(2))/((u-f)^(2))`
`rArr" "|(dv)/(du)|=(f^(2))/((u-f)^(2))" {Lateral magnification}"`
`rArr" "Deltav=(f^(2))/((u-f)^(2))Deltau`
`rArr" Image length"=(f^(2))/((u-f)^(2))xx"object length"`
`"Image length"=(f^(2)L)/((u-f)^(2))`
Note that is above calculation object length along the principal axis is assumed to be very small.