Question

An infinitely long rod lies along the axis of a concave mirror of focal length $f$. The near end of the rod is at a distance $u>f$ from the mirror. Its image will have a length

• A. $\frac{uf}{u-f}$
• B. $\frac{uf}{u+f}$
• C. $\frac{f^2}{u+f}$
• D. $\frac{f^2}{u-f}$

Answer 1

The correct option is D $\frac{f^2}{u-f}$

For near end of the rod, applying mirror formula,
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Here, $u$ and $f$ both are negative.
Therefore, distance of image of near end of the rod from the pole is :
$|v|=\frac{uf}{u-f}$

where $u$ & $f$ are the magnitudes of the respective quantities.

Far end of the rod is at infinity. Therefore, its image will be formed at focus.

$\therefore$ Length of the image $=|v|-f$
$=\frac{uf}{u-f}-f$
$=\frac{f^2}{u-f}$