Question

An object of height 2 cm is placed at a distance of 20 cm in front of a concave mirror of a focal length of 12 cm. Find the position, size, and nature of the image.

Answer 1

The image is 30 cm in front of the mirror, 3 cm high, real, inverted and magnified.

Answer 2

Object distance (u) = -20 cm

Focal length (f) = -12 cm

Image size (I) = 2 cm

Let the image distance be 'v' then

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

Or, `1/(-20) + 1/v = 1/(-12)`

Or, `1/v = -1/12 + 1/20 = (-5 + 3)/60`

Or, `1/v = -2/60`

Or, v = -30 cm

Now, `"Image size (I)"/"Object size (O)" = -"Image distnace (v)"/"Object distnace (u)"`

Or, `I/2 = -((-30)/-20)`

Or, I = -3 cm

∴ The image is 30 cm in front of the mirror.

The image is 3 cm high with the following characteristics:

• Real
• Inverted
• Magnified