Question

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

Answer 1

Magnification $m=\frac{h_I}{h_O}$

$m=\frac{-4}{1}=-4$

Here, $u=-20cm$

Magnification can also be written as:

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

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

$v=-80cm$

Thus image distance is $80cm$.

Now, Using mirror formula,

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

$\frac{1}{f}=\frac{1}{-80}+\frac{1}{-20}=\frac{-5}{80}$

hence, $f=-16cm$