An object of length 4 cm is placed in front of a concave mirror at a distance 30 cm. The focal length of mirror is 15 cm. (a) Where will the image form? (b) What will be the length of image?

u = 30 cm (negative)

f = 15 cm (negative)

Mirror formula:

1\over u + 1\over v = 1\over f

⇒ – 1\over 30 + 1\over v = – 1\over 15

⇒ 1\over v = – 1\over 15 + 1\over 30

⇒ 1\over v = -2 + 1\over 30

⇒ 1\over v = -1\over 30

⇒ v = 30 cm

Hence, the image is formed at 30 cm in front of the mirror

(b) Magnification

Image\ size \over Object\ size = Image\ distance \over Object\ distance

⇒ I \over 4 =- 30 \over 30

⇒ I = – 30 \over 30 × 4 = – 4 cm

Hence, length of image = 4 cm

Negative sign represents that the image is inverted.