MCQ
The relation between the linear magnification $m$, the object distance $u$ and the focal length $f$ is
- A$m=\frac{f-u}{f}$
- ✓$m=\frac{f}{f-u}$
- C$m=\frac{f+u}{f}$
- D$m=\frac{f}{f+u}$
✓
Answer
Correct option: B.
$m=\frac{f}{f-u}$
$ \because m=-\frac{v}{u} \text { also } \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \Rightarrow \frac{u}{f}=\frac{u}{v}+1 $
$ \Rightarrow-\frac{u}{v}=1-\frac{u}{f} \Rightarrow \frac{-v}{u}=\frac{f}{f-u} \text { so } m=\frac{f}{f-u} .$
$ \Rightarrow-\frac{u}{v}=1-\frac{u}{f} \Rightarrow \frac{-v}{u}=\frac{f}{f-u} \text { so } m=\frac{f}{f-u} .$
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