Question

An object 1.5 cm high when placed in front of a concave. the mirror produces a virtual image 3 cm high. If the object is placed at a distance of 6 cm from the pole of the mirror, calculate:

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

Answer 1

Size of object = h₀ = 1.5 cm

Size of image = h₁ = + 3 cm   [Image formed by a concave mirror is virtual]

Distance of the object from the pole of the mirror = u = - 6 cm

(i) Distance of the image from the pole of mirror = v = ?

Linear magnification = m = `"h"_1/"h"_0 = - "v"/"u"`

`(+3)/1.5 = - "v"/-6`

v = `+ (6 xx 3)/1.5`

v = + 12 cm

So, image is formed at a distance of 12 cm behind the concave mirror.

(ii) Focal length of the concave mirror = f = ?

Using mirror formula:

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

`1/-6 + 1/(+12) = 1/"f"`

`1/"f" = - 1/6 + 1/12 = (- 2 +1)/12 = -1/12`

⇒ f = - 12 cm