Question

A converging mirror forms a real image of height $4cm$ of an object of height $1cm$ placed $20cm$ away from the mirror. Calculate focal length of the mirror.

Answer 1

Given,

Height of the image = 4 cm

Height of the object = 1 cm

So the magnification will be 4

Now,

We know that

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

Putting all the values

$-4=\frac{-v}{-20}$

$v=-80cm$

Image distance is - 80 cm

Now we know from the mirror formula

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

Putting all the values

$\frac{1}{-80}+\frac{1}{-20}=\frac{1}{f}$

$\frac{1}{f}=\frac{1+4}{-80}$

$f=-16cm$

Thus focal length of converging mirror is 16 cm.