Physics - Geometrical Optics Question with Solution | TestHub

Given: Focal length $f=-12$ cm (concave mirror), object distance $u=-20$ cm, object velocity $v_o=4$ cm/s.

Mirror formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$.

Differentiating with respect to time: $0=-\frac{1}{v^2}\frac{dv}{dt}-\frac{1}{u^2}\frac{du}{dt}$.

So, $v_i=-\frac{v^2}{u^2}{v}_o$.

From mirror formula: $\frac{1}{-12}=\frac{1}{v}+\frac{1}{-20}⟹\frac{1}{v}=\frac{1}{20}-\frac{1}{12}=\frac{3-5}{60}=-\frac{2}{60}=-\frac{1}{30}$. So $v=-30$ cm.

$v_i=-{\left(\frac{-30}{-20}\right)}^2(4)=-{\left(\frac{3}{2}\right)}^2(4)=-\frac{9}{4}(4)=-9$ cm/s.

The velocity of the image is 9 cm/s towards the mirror.