Question

An object placed 20 cm in front of a mirror is found to form an image of 15 cm.1. in front of it (2) behind the mirror .Find the focal length of mirror and the kind of mirror in each case

Answer 1

An object placed 20 cm in front of a mirror is found to have an image 15 cm (a) in front of it, (b) behind the mirror. Find the focal length of the mirror............

Answer 2

Answer:

(a) u = -20cm, v = -15cm

We know that

$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

⇒ $\dfrac{1}{-15} + \dfrac{1}{-20} = \dfrac{1}{f}$

⇒ $\dfrac{1}{f} = - \dfrac{ 1}{15} - \dfrac{1}{20} = \dfrac{(-4 - 3)}{60} = - \dfrac{7}{60}$

$\therefore f = - \dfrac{60}{7} cm$

The mirror is a concave mirror.

(b) u = -20cm, v = 15cm

We know that

$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

⇒$\dfrac {1}{15} + \dfrac{1}{-20} = \dfrac{1}{f}$

⇒ $\dfrac{1}{f} = \dfrac{1}{15} - \dfrac{1}{20} = \dfrac{(4 - 3)}{60} = \dfrac{1}{60}$

∴ f = 60 cm

The mirror is a convex mirror.