A point object is between the Pole and Focus | vedclass

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(A) For a concave mirror,the mirror formula is given by $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Differentiating with respect to time $t$,we get $-\f

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away from mirror and increasing in magnitude

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(A) For a concave mirror,the mirror formula is given by $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Differentiating with respect to time $t$,we get $-\frac{1}{v^2} \frac{dv}{dt} - \frac{1}{u^2} \frac{du}{dt} = 0$.Thus,the velocity of the image $v_i = \frac{dv}{dt} = -(\frac{v}{u})^2 \frac{du}{dt}$.Here,the object is between the Pole $(P)$ and Focus $(F)$,so $u As the object moves away from the mirror,$u$ increases (becomes less negative),and the image also moves away from the mirror ($v$ increases).The magnification $m = \frac{v}{|u|} = \frac{f}{f-u}$. As $u$ increases towards $f$,the magnitude of $m$ increases rapidly.Since $v_i = -m^2 v_o$,and $m$ increases as the object moves away from the mirror,the magnitude of the image velocity $|v_i| = m^2 |v_o|$ increases.Therefore,the image moves away from the mirror with an increasing magnitude of velocity.

$A$ point object is between the Pole and Focus of a concave mirror,and moving away from the mirror with a constant speed. Then,the velocity of the image is:

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