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  4. A convex mirror has a focal length f. A real object is placed at a distance f in front of it, from the pole. It produces an image at

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Q. A convex mirror has a focal length $f$. A real object is placed at a distance $f$ in front of it, from the pole. It produces an image at

Ray Optics and Optical Instruments

Solution:

Mirror formula: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Here object is real so $u$ is negative
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Also $(u)=f$
$\frac{1}{v}-\frac{1}{f}=\frac{1}{f} $
$\therefore v=\frac{f}{2}$