Question

A concave mirror forms a virtual image of size twice that of the object placed at a distance 5 cm from it. Find:

1. the focal length of the mirror
2. position of image

Answer 1

Given: Object distance, u = −5 cm (object is in front of the mirror)

The image is virtual and erect

Magnification, m = +2m

(a) m = `-v/u`

∴ `-v/u = 2`

∴ −v = 2u

∴ −v = 2 × −5

∴ v = 10 cm

Hence, the image is 10 cm behind the mirror.

(b) From the mirror formula,

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

∴ `1/f = 1/10 + 1/(-5)`

= `1/10 - 1/5`

∴ f = −10 cm