Question

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 ______.

Options

• –30 cm

• –20 cm

• –40 cm

• –60 cm

Answer 1

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

∴ `1/f = 1/u + 1/v`

= `-1/60 - 1/30`

= `-1/20` or

f = −20 cm