Question

The image formed by a convex mirror is only one-third of the size of the object. If the focal length of the mirror is $12\text{cm}$, then the position of the image formed will be

• A. $8\text{cm}$ behind the mirror
• B. $10\text{cm}$ behind the mirror
• C. $8\text{cm}$ in front of the mirror
• D. $10\text{cm}$ in front of the mirror

Answer 1

The correct option is A $8\text{cm}$ behind the mirror

We know magnification $m=-\frac{v}{u}=\frac{1}{3}$
Hence, $u=-3v$
Given that focal length of the mirror is $f=+12\text{cm}$
Applying mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-3v}=\frac{1}{12}$
$\Rightarrow v=+8\text{cm}$