Question

An object 2 cm high is placed at right angles to the principal axis of a mirror of focal length 25 cm such that an
erect image 6 cm high is formed by it. Then the type of mirror and the position of object are:​

Answer 1

Given:

An object 2 cm high is placed at right angles to the principal axis of a mirror of focal length 25 cm such that an erect image 6 cm high is formed by it.

To find:

• Type of mirror

• Object distance

Calculation:

The type of image formed is virtual and magnified. This is possible only in case of concave mirror.

Now ,we can say :

$\therefore \: \dfrac{ h_{i}}{h_{o}} = - \dfrac{v}{u}$

$= > \: \dfrac{6}{2} = - \dfrac{v}{u}$

$= > \: 3 = - \dfrac{v}{u}$

$= > \: v = - 3u \: \: \: \: \: .......(1)$

Applying mirror formula:

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

$= > \: \dfrac{1}{( - 25)} = \dfrac{1}{v} + \dfrac{1}{u}$

$= > \: \dfrac{1}{( - 25)} = \dfrac{1}{( - 3u)} + \dfrac{1}{u}$

$= > \: - \dfrac{1}{ 25} = - \dfrac{1}{3u} + \dfrac{1}{u}$

$= > \: - \dfrac{1}{ 25} = \dfrac{ - 1 + 3}{3u}$

$= > \: - \dfrac{1}{ 25} = \dfrac{ 2}{3u}$

$= > u = - \dfrac{75}{2}$

$= > u = - 37.5 \: cm$

So, object is placed 37.5 cm in front of mirror.