Question

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

Answer 1

given ,
focal length (f ) = - 12 cm
object distance ( u ) = -20 cm
use formula ,
1/u + 1/ v = 1/ f

1/(-20) + 1/v = 1/(-12)

1/v = 1/20 - 1/12

=-8/20 x 12 = - 1/30

v = - 30 cm

hence image form 30 cm distance from the pole of mirror from left side .

m = -v/u = height of image / height of object

-(-30)/(-20) = height of image /2 cm

height of image = -3 cm

hence image form left side from the pole below the x -axis and image is real inverted and larger then object .

Answer 2

Answer:

Explanation:

Given:-

h(o) = 2 cm

f = - 12 cm

u = - 20 cm

Formula to be used :-

Mirror Formula i.e 1/f = 1/v + 1/u

Magnification, m = h(i)/h(o) = - v/u

Solution :-

Putting all values, we get

1/f = 1/v + 1/u

⇒ 1/- 12 = 1/v + 1/- 20

⇒ 1/v = - 5 + 3/60

⇒ 1/v = - 2/60

⇒ 1/v = - 1/30 cm

⇒ v = - 30 cm

Magnification, m = h(i)/h(o) = - v/u

⇒ m = - v/u

⇒ m = 30/- 20

⇒ m = - 1.5

Now, h(i) = - 1.5 × 2 = - 3 cm.

Image will be real, inverted and magnified.