Question

The relation between the linear magnification m, the object distance $u$ and the focal length $f$ is

• A. $m=\frac{f-u}{f}$
• B. $m=\frac{f}{u-f}$
• C. $m=\frac{f+u}{f}$
• D. $m=\frac{f}{f+u}$

Answer 1

Answer: (B)

$m=\frac{f}{u-f}$

The linear magnification can be given as

$m=\frac{v}{u}\Rightarrow v=mu$

Now the mirror formula is given as

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

Substituting $v=mu$ in mirror formula

$\Rightarrow \frac{1}{f}=\frac{1}{mu}+\frac{1}{u}\Rightarrow \frac{1}{f}=\frac{1+m}{mu}$

$\Rightarrow \frac{mu}{f}-m=1\Rightarrow m\left(\frac{u}{f}-1\right)=1$

$\Rightarrow m\left(\frac{u-f}{f}\right)=1$

Therefore,

$m=\frac{f}{u-f}$