Question

A 2.0 cm high object is placed at a distance of 20 cm from a concave mirror. A real image is formed 40 cm from the mirror. Calculate the focal length of the mirror and the size of the image.

Answer 1

Step 1: Given that:

Height of object($h_o$ )= $2cm$

Object distance($u$ )= $-20cm$

Image distance($v$ )= $-40cm$

( As, the image is real, it means the image is formed in front of the mirror.)

Step 2: Formula used:

Mirror formula is given as;

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

Where, $f$ is the focal length of the mirror.

Magnification of the mirror is given by;

$m=\frac{h_i}{h_o}=-\frac{v}{u}$

Step 3: Calculation of focal length of the concave mirror:

$\frac{1}{f}=\frac{1}{-40cm}+\frac{1}{-20cm}$

$\frac{1}{f}=-\frac{1}{40}-\frac{1}{20}$

$\frac{1}{f}=\frac{-1-2}{40}$

$\frac{1}{f}=\frac{-3}{40}$

$f=\frac{-40}{3}cm$

Step 4: Calculation of size of the image:

$\frac{h_i}{2cm}=-\frac{-40cm}{-20cm}$

$h_i=-2\times 2$

$h_i=-4cm$

(Negative sign indicates that the image is inverted.)

Hence,

The focal length of the concave mirror= $\frac{40}{3}cm$

Size of the image= $4cm$