Question

A concave mirror forms a real image of an object placed in front of it at a distance 30 cm, of size three times the size of object. Find

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

Answer 1

u = −30 cm

m = `I/O = 30/O = 3`

But, for real object m is negative

∴ m = −3

∵ m = `-v/u`

∴ `-v/u = -3`

∴ v = 3u

∴ v = 3 × −30

∴ v = −90 cm

Hence, the position of the image is 90 cm in front of the mirror.

From mirror formula,

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

∴ `1/f = 1/(-90) + 1/(-30)`

= `-1/90 - 1/30`

= `(-1 - 3)/90`

= `(-4)/90`

∴ f = −22.5 cm