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

Answer 1

Answer: (D)

since the rod is infinitely long the image of end $B$ will be formed at focus. Image of $A$ can be found using $\frac{1}{v}+\frac{1}{\left(\right. - u \left.\right)}=\frac{1}{- f}$
So $v=\frac{fu}{f - u}$
This $V$ is position of image and we know image of $A$ will be real hence distance of image $=\frac{f u}{u - f}$
so the size of image $=\frac{f u}{u - f}-f$
$=\frac{f u - f u + f^{2}}{u - f}=\frac{f^{2}}{u - f}$