A point object is moving on the principal axi | vedclass

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(C) For a concave mirror,the mirror formula is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given: Focal length $f = -24\;cm$ (sign convention f

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$4\;cm/sec$ towards the mirror

Vedclass · Answer

(C) For a concave mirror,the mirror formula is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given: Focal length $f = -24\;cm$ (sign convention for concave mirror),object distance $u = -60\;cm$.Substituting the values: $\frac{1}{-24} = \frac{1}{v} + \frac{1}{-60}$.$\frac{1}{v} = \frac{1}{60} - \frac{1}{24} = \frac{2 - 5}{120} = \frac{-3}{120} = -\frac{1}{40}$.So,$v = -40\;cm$.Differentiating the mirror formula with respect to time $t$: $-\frac{1}{v^2} \frac{dv}{dt} - \frac{1}{u^2} \frac{du}{dt} = 0$.Therefore,the velocity of the image $v_i = \frac{dv}{dt} = -(\frac{v}{u})^2 \frac{du}{dt}$.Given $\frac{du}{dt} = -9\;cm/s$ (moving towards the mirror).$v_i = -(\frac{-40}{-60})^2 	imes (-9) = -(\frac{2}{3})^2 	imes (-9) = -(\frac{4}{9}) 	imes (-9) = 4\;cm/s$.The positive sign indicates the image is moving in the same direction as the object,which is towards the mirror.

$A$ point object is moving on the principal axis of a concave mirror of focal length $24\;cm$,towards the mirror. When it is at a distance of $60\;cm$ from the mirror,its velocity is $9\;cm/sec$. What is the velocity of the image at that instant?

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