Question

A convex mirror has a focal length $f$. A real object is placed in front of it, at a distance $f$ from the pole. At what distance from the pole the image will be formed :

• A. Infinity
• B. $f$
• C. $\frac{f}{2}$
• D. $2f$

Answer 1

The correct option is C $\frac{f}{2}$


In case of real object placed in front of convex mirror at a distance $f$.
According to sign convention,
Position of object, $u=-f$
Focal length, $f=+f$
Applying mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}+\frac{1}{(-f)}=\frac{1}{f}$
$\frac{1}{v}=\frac{2}{f}$
$\therefore v=\frac{f}{2}$
The positive sign of $v$ indicates image is formed behind the mirror.