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?

Apply the relation – (v / u) = m = hi / ho as

= (- 5) / 10

= – {(- 30) / u}

=u = – 60 cm

Apply mirror formula as

= (1 / v) + (1 / u)= 1 / f

= 1 / (- 60) + 1 / (- 30)= 1 / f

= 1 / (- 20) = 1 / f or f = – 20 cm

Hence, b) -20 cm is the answer. The focal length lies in front of the mirror. Therefore, the sign is negative.

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