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 (a) the focal length of mirror (b) 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