A point object moves along the principal axis of a convex lens of focal length `f`, such that its image also formed on the principal axis at a distance `(4f)/(3)` (at `t=0`) moves away from the lens with a uniform velocity `alpha`. Find the velocity of point source as a function of time `t`.

Explanation

`(v_i)/(v_O)=((v)/(u))^2=((f-v)/(f))^2`
`(alpha)/(v_O)=((f-(4f)/(3)-alphat)^2)/(f^2)=((f)/(3)-alphat)^(2)/(f^2)`
`v_(0)=(f^(2)alpha)/((f/3-alphat)^(2))`