Question

The focal length of a concave mirror is $30cm$. Find the distance of the object in front of the mirror, so that the image is three times the size of the object.

• A. $40cm,20cm$
• B. $30cm,50cm$
• C. $60cm,80cm$
• D. $25cm,15cm$

Answer 1

The correct option is A $40cm,20cm$

Using mirror formula,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
i.e $v=\frac{uf}{u-f}$
and magnification $m=\frac{h_i}{h_o}=\frac{-v}{u}=\frac{f}{f-u}$
Since a concave mirror can form both real & virtual image, we have to consider two cases.

Case 1: Image is inverted


In this case, $m=-3=\frac{f}{f-u}=\frac{-30}{-30-u}$
$\Rightarrow u=-40cm$

Case 2: Image is erect


$m=3=\frac{f}{f-u}=\frac{-30}{-30-u}$
$\Rightarrow u=-20cm$