Question

The object distance u, the image distance v and the magnification m in a lens follow certain linear relations. These are

• A. $\frac{1}{u}$ versus $\frac{1}{v}$
• B. m versus u
• C. u versus v
• D. m versus $\frac{1}{u}$

Answer 1

The correct option is A $\frac{1}{u}$ versus $\frac{1}{v}$

For a lens $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}....\left(i\right)$
Also $m=\frac{f-v}{f}=1-\frac{v}{f}\Rightarrow m=(-\frac{1}{f})v+1...\left(ii\right)$
On comparing equations (i) and (ii) with y =mx +c.
It is clear that relationship between $\frac{1}{v}vs\frac{1}{u}$ and m vs v is linear.