First slide

Spherical/Curved mirrors

Question

When an object is kept at a distance of 30cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cm $s^{- 1}$ , the speed (in cm $s^{- 1}$ ) with which image moves at the instant is ___

Moderate

Solution

$\begin{array}{l} M i r r o r F o r m u l a, \\ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \Rightarrow \frac{1}{v^{2}} \frac{dv}{dt} = - \frac{1}{u^{2}} \frac{d u}{dt} \\ \Rightarrow \frac{dv}{dt} = - \frac{v^{2}}{u^{2}} \frac{d u}{dt} \\ ∴ \frac{dv}{dt} = - {(\frac{10}{30})}^{2} (9) \\ \Rightarrow |\frac{dv}{dt}| = 1 cm / \sec \end{array}$

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