# 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

h = 10 mm = 1 cm

Size of the image h₁ = 5 mm = 0.5 cm

Distance of image from the pole of mirror v = – 30 cm

Let distance of object = u

Focal length = f

Using mirror formula

1/v + 1/u = 1/f

Therefore, the value of “u” is needed for that magnification formula will be used:

Magnification (m) = h₁/h = – v/u

1/f = 1/v + 1/u

Putting all the values in mirror formula:

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[B] – 20 cm

Putting all the values in mirror formula:

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

Or, 2+1/-60 = 1/f

1/f = 3/-60

Or, f = -20 cm