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 (A) 30 cm (B) 20 cm (C) 40 cm (D) 60 cm

Answer – The  Correct option is (B) 20cm. 

Focal length of concave mirror is – 

1/f = 1/v + 1/u

Here, according to the question 

v=-30cm

Magnifying factor (m) = m/u = -y/x

m = -5/10

Since m = v/u

-5/10 = v/u

-5/10 = (-30)/u

∴ u = 60cm

Also, the object distance is always negative,

Therefore u= -60cm.

Applying the formula,

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

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

1/f= -1/60 – 1/30

1/f=-90/1800

f = – 20 cm

Since the focal length is in front of the mirror, its sign is negative.