Discussion
A real object is placed at distance of \(f\) in front of a convex mirror of focal length\(f\). The image will be formed at a distance
Answer: E
The image is formed at a distance \(\frac{f}{2}\).
Using the mirror formula with the Cartesian sign convention, the object distance is \(u = -f\) and a convex mirror has focal length \(+f\):
\[ \begin{aligned} \frac{1}{v} + \frac{1}{u} &= \frac{1}{f} \\ \frac{1}{v} &= \frac{1}{f} + \frac{1}{f} = \frac{2}{f} \Rightarrow v = \frac{f}{2} \end{aligned} \]
The image is virtual, behind the mirror, halfway between pole and focus. Taking the convex mirror's focal length as negative leads to an infinite or wrong distance; 2f and f are concave-mirror reasoning.
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