A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is ______.

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A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is –20 cm. Explanation: m = h^'/h = (-v )/u or u = ((-v) xx h)/h^' `= (-(-30 cm) xx (10 mm))/(-5 mm) = −60 cm $\therefore$ 1/f = 1/u + 1/v = -$\frac{1}{60}$ - $\frac{1}{30}$ = -$\frac{1}{20}$` or f = −20 cm

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