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What is the velocity (in cm $s^{- 1}$ ) of image in situation shown in figure. (O=object, $f = f o c a l$ length). Object moves with velocity 10 cm/s and mirror moves with velocity 2 cm $s^{- 1}$ as shown.

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Detailed Solution

$\frac{1}{y} + \frac{1}{- x_{1}} = \frac{1}{10} ....... (i)$

$\frac{1}{y} - \frac{1}{10} = \frac{1}{10} \Rightarrow y = 5 c m$

$\frac{d x}{d t} = 10 c m s^{- 1}, \frac{d (x + x_{1})}{d t} = 2 c m s^{- 1}$

$\frac{d x_{1}}{d t} = - 8 c m s^{- 1}$

$\frac{d y}{d t} = v_{i} = 2$

From (i): $\frac{d y}{d t} = {(\frac{y}{x_{2}})}^{2} \frac{d x_{1}}{d t}$

$\Rightarrow v_{i} - 2 = {(\frac{5}{10})}^{2} (- 8) \Rightarrow v_{i} = 0$

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