Question

A short linear object of length $I$ lies along the axis mirror of focal length $F$ at a distance u form the of the mirror. The size of the image is approximately equal to:

• A. $I{\left(\frac{u-f}{f}\right)}^{1/2}$
• B. $I{\left(\frac{u-f}{f}\right)}^2$
• C. $I{\left(\frac{f}{u-f}\right)}^{1/2}$
• D. $I\left(\frac{f}{u-f}\right)$

Answer 1

The correct option is D $I\left(\frac{f}{u-f}\right)$

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

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

$v=\frac{fu}{u-f}$

We have magnification , $m=\frac{I^{\prime }}{I}=\frac{-v}{u}$

$I^{\prime }=-I\left(\frac{fu}{u(u-f)}\right)=I\left(\frac{f}{f-u}\right)$