Question

A converging mirror, forms three times magnified virtual image when an object is placed at a distance of 8 cm from it. Calculate:

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

Answer 1

Let size of the object = h_o = x
Size of image = h₁= +3 x (Virtual image)
Distance of the object from the mirror = u = -8 cm
Distance of the image from the mirror = v = ?
Focal length of the mirror = f = ?

(i) Magnification = m = `"h"_1/"h"_0 = - "v"/"u"`

`=> "3x"/"x" = "-v"/-8`

v = 8 × 3 = 24 cm

(ii) Using mirror formula:

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

`1/-8 + 1/24 = 1/"f"`

`1/"f" = - 1/8 + 1/24`

`1/"f" = (- 3 + 1)/24 = (-2)/24 = - 1/12`

⇒ f = - 12 cm