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)

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