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 $v$

Answer 1

Answer: (A), (D)

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 $y=mx+c$
It is clear that relationship between $\frac{1}{v}vs\frac{1}{u}$
and $mvsv$ is linear.