Question

A point object is moving at a speed of $v_0$ towards the spherical mirror. Calculate the speed of the image.

Answer 1

From mirror formula

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

differentiating w.r.t time

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

$\frac{dv}{dt}=$ velocity of image

$\frac{du}{dt}=$ velocity of object

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

But $\frac{v}{u}=\frac{f}{u-f}$

$\Rightarrow v_{image}=-{\left[\frac{f}{u-f}\right]}^2{v}_{object}$