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

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

Ray Optics and Optical Instruments

Solution:

$\because m=-\frac{v}{u}$ also $\frac{1}{f}=\frac{1}{v}+\frac{1}{u} \Rightarrow \frac{u}{f}=\frac{u}{v}+1$
$\Rightarrow -\frac{u}{v}=1-\frac{u}{f} \Rightarrow \frac{-v}{u}=\frac{f}{f-u}$ so $m=\frac{f}{f-u}$