Question

An object of height 8 cm is placed 24 cm in front of a concave mirror of focal length 12 cm. What is height of the image?

a) 8 cm

b) 12 cm

c) - 8 cm

d) - 12 cm​

Answer 1

Answer:

(a) 8 cm

Explanation:

Given that, an object is placed in front of a concave mirror.

Height of the object, h = 8 cm

Object Distance, u = -24cm

Focal length, f = 12 cm

To find the Height of the image, H.

Let the image distance be v.

We know that,

By mirror formula, we have,

1/u + 1/v = 1/f

Substituting the values, we get,

=> -1/24 + 1/v = -1/12

=> 1/v = 1/24 - 1/12

=> 1/v = 1/24 - 2/24

=> 1/v = -1/24

=> v = -24

Therefore, the image distance is 24 cm, on the same side of the object.

Now, we know that,

Magnification, m = -v/u = H/h

=> -(-24)/(-24) = H/8

=> H/8 = -1

=> H = -8

Hence, the size of image is (a) 8 cm, inverted ( denoted by the negative sign) and equal to the size of object.

Answer 2

Given :

•An object is placed in front of a concave mirror.

•Height of the object (h) = 8 cm

•Object Distance (u) = -24cm

•Focal length (f) = 12 cm

To Find :

•Height of the image .

SOLUTION :

Apply mirror formula,

1/u + 1/v = 1/f

[ Put the values, we get, ]

=> -1/24 + 1/v = -1/12

=> 1/v = 1/24 - 1/12

=> 1/v = 1/24 - 2/24

=> 1/v = -1/24

=> v = -24 cm.

Hence, the image distance is 24 cm .

As, we know that,

Magnification, m = -v/u = H/h

[ Put the values, we get ]

=> -(-24)/(-24) = H/8

=> -1 = H/8

=> H = -8cm .

Therefore, the size of image is (option a) 8 cm. ( Inverted denoted by the negative sign and equal to the size of object .)