Question

A linear object is placed along the axis of a mirror as shown in the figure. If $f$ is the focal length of the mirror, then the length of the image is

• A. $\frac{\left(2 f\right)}{3}$
• B. $f$
• C. $\frac{f}{3}$
• D. none

Answer 1

Answer: (B)

The image of object at $2f$ will be formed at $2f$ . So the object and image will coincide at $2f$ .


$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}-\frac{1}{\left(\frac{- 3 f}{2}\right)}=\frac{1}{f}$
$\frac{1}{v}=\frac{1}{f}-\frac{2}{3 f}=\frac{1}{3 f}$
$\therefore $ Length of image $=3f-2f=f$