Speed of image formed by a spherical mirror related to speed of object.

Using mirror formula,

$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$,

where $f$ is constant

Differentiating both sides w.r.t. 't', we get

$\frac{d}{dt}(\frac{1}{u} + \frac{1}{v})=\frac{d}{dt}(\frac{1}{f})$

$-\frac{1}{u^2} \frac{du}{dt} - \frac{1}{v^2} \frac{dv}{dt} = 0$

$ \frac{du}{dt} = -\left(\frac{u}{v}\right)^2 \frac{dv}{dt}$

Here $\frac{dv}{dt} = V_i$ is speed of image and $V_o = \frac{du}{dt}$ is speed of object.

$V_o = -\left(\frac{u}{v}\right)^2 V_i$

$V_i = -\left(\frac{v}{u}\right)^2 V_o$

$V_i = -\left(\frac{f}{u-f}\right)^2 V_o$