A convex mirror has a focal length f. A real object placed at a distance f in front of it produces an image at
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( f/2 \)
The image follows from the mirror equation \( 1/v+1/u=1/f \) with the Cartesian sign convention. The focus of a convex mirror lies behind it, so its focal length \( f \) is positive. The real object in front of it has \( u=-f \).
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= \frac{1}{f}+\frac{1}{f} \\ &= \frac{2}{f} \end{aligned} \)
\( v=f/2 \)
The positive sign places the image at a distance \( f/2 \) behind the mirror, midway between the pole and the focus. So it is a virtual image.