Question

A beam of light converges towards a point $O$, behind a convex mirror of focal length $10cm$. Find the nature and position of image, if the point $O$ is-
(i) $5cm$ behind the mirror
(ii) $15cm$ behind the mirror

Answer 1

Given: A beam of light converges towards a point O, behind a convex mirror of focal length 10cm.

To find the nature and position of image, if the point O is (i) 5cm behind the mirror (ii) 15cm behind the mirror

Solution:

Case (i): when point O is 5cm behind the mirror

According to the given criteria,

object distance, $u=-5cm$

focal length, $f=-10cm$

Applying the mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{(-10)}-\frac{1}{(-5)}⟹\frac{1}{v}=\frac{-1+2}{10}⟹v=10cm$

Hence the image is at a distance of 10 cm in-front of the convex mirror.

Magnification, $m=-\frac{v}{u}=-\frac{10}{(-5)}=+2$

Nature of the image: virtual, erect and enlarged.

Case (ii): when point O is 15 cm behind the mirror

According to the given criteria,

object distance, $u=-15cm$

focal length, $f=-10cm$

Applying the mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{(-10)}-\frac{1}{(-15)}⟹\frac{1}{v}=\frac{-3+2}{30}⟹v=-30cm$

Hence the image is at a distance of 30 cm behind the convex mirror.

Magnification, $m=-\frac{v}{u}=-\frac{(-30)}{(-15)}=-2$

Nature of the image: Real, inverted and enlarged.