Question

A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature and position of the image formed.

Answer 1

Focal length = f = - 4 cm
Height of object = + 2 cm
Object distance = u = - 9 cm
Image distance = v = ?
Height of image = size = h' = ?

From thew mirror formula

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

Putting all the values

$\frac{1}{v}-\frac{1}{9}=\frac{1}{-4}$

After solving

$v=-7.2cm$

Hence, the image is formed at a distance of 7.2 cm from the mirror.

Now for finding magnification

We know,

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

Putting all the values

$\frac{-(-7.2)}{-9}$

After solving

$m=-0.8$

As the magnification is negative, the image is real, inverted.