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Q.
The object distance $u$, the image distance $v$ and the magnification $m$ in a lens follow certain linear relations. These are
Ray Optics and Optical Instruments
Solution:
For a lens $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$ \Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}$ ... (i)
Also $m=\frac{f-v}{f}=1-\frac{v}{f}$
$ \Rightarrow m=\left(-\frac{1}{f}\right) v+1$ ....(ii)
On comparing equations (i) and (ii) with $y=m x+c$
It is clear that relationship between $\frac{1}{v} v s \frac{1}{u}$
and $m \,v s\, v$ is linear.