Question

The linear magnification for a mirror is the ratio of the size of the image to the size of the object, and is denoted by $m$. Then $m$ is equal to (symbols have their ususal meanings)

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

Answer 1

Answer: (C)

$m=\frac{h_1}{h_0}=\frac{-v}{u}......\left(i\right)$
From mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}........\left(ii\right)$
Multiplying equation (ii) by $u$, we get
$\frac{u}{f}=\frac{u}{v}+1$ or $\frac{u}{v}=\frac{u}{f}-1=\frac{u-f}{f}$
or $\frac{v}{u}$ or $m=-\frac{v}{u}=\frac{-f}{u-f}=\frac{f}{f-u}$