Question

A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.

Answer 1

Given: The object is kept 10 cm in front of the mirror, so u = −10 cm

A virtual image in a concave mirror is always erect, so the magnification is positive. Two-fold magnification, m = +2

Using the magnification formula for mirrors:

m = `-v/u`

2 = `-v/-10`

2 = `v/10`

v = 2 × 10

v = 20

The positive sign indicates the virtual image is formed 20 cm behind the mirror.

By using the mirror formula:

`1/f = 1/v + 1/u`

= `1/20 + 1/-10`

= `1/20 - 1/10`

= `1/20 - 2/20`

= `(1 - 2)/20`

`1/f = -1/20`

f = −20 cm

The focal length of the concave mirror is −20 cm. The negative sign confirms the mirror is concave.