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: (b) – 20 cm

Given parameters

size of object (O) = + 10.0 mm = + 1.0 cm (as, 1 cm = 10 mm)

Size of Image (I) = 5.0 mm = 0.5 cm

Image distance (v) = -30 cm (as image is real)

Let, object distance = u

Focal length, f =?

Magnification can be calculated using the formula

m= I(size of image)/O(size of image)

m= -v/u

I/O = -v/u

0.5/1 = -30/u

u = -60cm

Focal length is given by

1/f = 1/v + 1/u

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

1/f = (-2-1)/60

1/f = -3/60

f = -20cm

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