A concave mirror produces an image of a long vertical pin, placed 40cm from the mirror, at the position of the object. Find the focal length of the mirror.

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Detailed Solution

$\begin{array}{l} u = - 40 cm, v = - 40 cm, f = ? \\ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{1}{f} = - \frac{1}{40} - \frac{1}{40} = - \frac{2}{40} = - \frac{1}{20} \\ f = - 20 cm \end{array}$

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