A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it. When its distance from mirror is 20 cm its velocity is $4\text{cm/s}$ . The velocity of the image in $\text{cm/s}$ at that instant is :

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

Differtiating w.r.to time

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

Here$\frac{\text{du}}{\text{dt}}=+4\text{cm}$

$\text{u}=-\text{20 cm}$

$\frac{\text{dv}}{\text{dt}}=?$

Mirror formula

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

$\frac{\text{1}}{\text{v}}+\frac{1}{20}=-\frac{1}{12}$

$\text{v}=30\text{cm}$

$\frac{\text{dv}}{\text{dt}}=-\frac{{\left(-30\right)}^2}{{\left(-20\right)}^2}\left(+4\right)=-9\text{cm/s}$

So Image moving at 9cm/s away from the mirror