A particle is moving at a constant speed V from a large distance towards a concave mirror of radius R along its principal axis. Find the speed of the image formed by the mirror as a function of the distance x of the particle from the mirror.

Explanation

Given `(dx)/(dt)=V`

`1/v+1/u=1/f`
`1/v-1/x=(-2)/R`
`1/v=1/x-2/R=(R-2x)/(xR)`
`v=(xR)/(R-2x)`
`(dv)/(dt)=((R(dx)/(dt))(R-2x)+xR(2(dx)/(dt))/((R-2x)^2)`
`=(dv)/(dt)=(R^2(dx)/(dt))/((2x-R)^2)=(R^2V)/((2x-R)^2)