Question

An object is kept in front of a concave mirror of focal length 20cm . The image is three times the size of the distance . Calculate two possible distances of the object from the mirror.

Answer 1

$\huge{\boxed{\sf{Answer}}}$

Given : focal length = -20cm   ( sign convention )

Height of the image = 3h₀

For real image : m = -v/u = -3

⇒ v = 3u

Using mirror formula, 1/f = 1/v + 1/u

⇒ 1/-20 = 1/3u + 1/u

⇒  u = -80/3 cm

Foer a virtual image : m = -v/u = +3

⇒ v = -3u

Using mirror formula, 1/f = 1/v + 1/u

⇒ 1/-20 = 1/-3u + 1/u

u = -40/3 cm

 

∴ The two possible positions of the object are -80/3 cm

    and -40/3 cm.