Question

The graph between object distance u and image distance v for a lens is given below. The focal length of the lens is

• A. $5\pm 0.1$
• B. $5\pm 0.05$
• C. $0.5\pm 0.1$
• D. $0.5\pm 0.5$

Answer 1

Answer: (B)

$5\pm 0.05$

Answer 2

From the lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ we have,
$\frac{1}{f}=\frac{1}{10}-\frac{1}{-10} or f=+5$
Further, \hspace15mm \Delta u=0.1
\hspace15mm \Delta v=0.1 \hspace15mm (from the graph)
Now, differentiating the lens formula, we have
\hspace15mm \frac{\Delta f}{f^2}=\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}
\hspace15mm \Delta f=\Bigg(\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}\Bigg)
Substituting the values, we have
\hspace15mm \Delta f=\Bigg(\frac{0.1}{10^2}+\frac{0.1}{10^2}\Bigg)(5)^2 =0.05
\therefore \hspace15mm f\pm \Delta f=5\pm 0.05