Question

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

• A. $\frac{2f}{3}$
• B. $f$
• C. $\frac{f}{3}$
• D. None of these

Answer 1

The correct option is B $f$

For $A$
$u=-\frac{3f}{2}$
using mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}-\frac{2}{3f}=-\frac{1}{f}$
$\frac{1}{v}=\frac{2}{3f}-\frac{1}{f}$
$v=-3f$
Image of $A$ is at $3f$ from pole of mirror.

For $B$
$u=-2f$
using mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}-\frac{1}{2f}=-\frac{1}{f}$
$\frac{1}{v}=\frac{1}{2f}-\frac{1}{f}$
$v=-2f$
Image of $B$ is at $2f$ from pole of mirror.
Length of image of $AB$ is $3f-2f=f$