Question

16, Size of the image of an object formed by a mirror having focal length of 20 cm is observed to
reduce to one-third of its size. At what distance the object has been placed from the mirror?
What is the nature of the image and the mirror?​

Answer 1

Given:-

Size of the image of an object formed by a mirror having focal length of 20 cm is observed to reduce to one-third of its size.

To Find:-

• At what distance the object has been placed from the mirror.
• What is the nature of the image and the mirror.

Solution:-

$\sf \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

In Case of Concave mirror:-

m=-1/3 and f=-20cm

$m = \frac{ - 1}{3} = \frac{ - v}{u}$

$= > v = \frac{u}{3}$

$= > \frac{1}{f} = \frac{3}{u} + \frac{1}{u}$

$= > \frac{ - 1}{20} = \frac{4}{u}$

$= > u = - 80cm$

∴The Image is real and inverted.

In Case the mirror is convex:-

m=1/3 and f=20cm

$m = \frac{ - v}{u} = \frac{1}{3}$

$= > v = \frac{ - u}{3}$

$= > \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$= > \frac{1}{f} = - \frac{3}{u} + \frac{1}{u}$

$= > \frac{1}{f} = \frac{ - 2}{u}$

$= > \frac{1}{20} = \frac{ - 2}{u}$

$= > u = - 40cm$

∴The Image is Virtual and erect.