Question

A candle flame, 1cm high is placed at a distance of 2 m from a wall. How far from the wall must a
concave mirror be placed so that it may form a 3cm high image of the object on the screen? Also
calculate the focal length of the mirror.​

Answer 1

Given:

A candle flame, 1cm high is placed at a distance of 2 m from a wall.

To find:

Distance from the wall must a concave mirror be placed so that it may form a 3 cm high image of the object on the screen?

Calculation:

In our case , the image has to be formed on the wall (i.e. screen), hence:

• Object distance = u

• Image distance = u + 2

Now, it's given that image height is 3 cm and object height is 1 cm;

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

$\implies \: \dfrac{ 3}{1} = - (\dfrac{u + 2}{u} )$

$\implies \: - 3u = u + 2$

$\implies \: - 4u = 2$

$\implies \: u = - 0.5 \: m$

So, distance of concave mirror from wall:

$\therefore \: d = u + 2 = 0.5 + 2 = 2.5 \: m$

Now, applying MIRROR FORMULA:

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

$\implies \: \dfrac{1}{f} = \dfrac{1}{ (- 2.5)} + \dfrac{1}{ (- 0.5)}$

$\implies \: \dfrac{1}{f} = - \dfrac{1}{ 2.5} - \dfrac{1}{ 0.5}$

$\implies \: \dfrac{1}{f} = - \dfrac{2}{5} - 2$

$\implies \: \dfrac{1}{f} = - \dfrac{12}{5}$

$\implies \: \dfrac{1}{f} = -2.4 \: m$

So, focal length is -2.4 metres.