A point object is moving with speed V0 towards a concave mirror with radius of curvature R, along the principal axis. The speed of the image is not defined when the object is :
⇒1v=−2R−1−u
⇒1v=−2u+RRu
⇒v=RuR−2u
And magnification (m) is given by
m=−vu
⇒m=−RuR−2u−u=RR−2u
For motion of the object along the principal axis,
velocity of image, Vi=−m2Vo
⇒Vi=−(RR−2u)2Vo .........(1)
Eq.(1) is not defined when R−2u=0
⇒u=R2 [at focus]
Hence, when the object is at focus, the speed of the image is not defined.