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

• A

  $\frac{\left(2\mathrm{f}\right)}{3}$
• Correct answer
  B

  $\mathrm{f}$
• C

  $\frac{\mathrm{f}}{3}$
• D

  none

Solution

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




$\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}$

$\frac{1}{\mathrm{v}}-\frac{1}{\left(\frac{-3\mathrm{f}}{2}\right)}=\frac{1}{\mathrm{f}}$

$\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}-\frac{2}{3\mathrm{f}}=\frac{1}{3\mathrm{f}}$

$\therefore$ Length of image $=3\mathrm{f}-2\mathrm{f}=\mathrm{f}$ 

Hence, the correct answer is option: 'B'.