Question

Graph of position of image versus position of point object from a convex lens is shown. Then, the focal length of the lens is

• A. $0.50\pm 0.05cm$
• B. $0.50\pm 0.10cm$
• C. $5.00\pm 0.05cm$
• D. $5.00\pm 0.10cm$

Answer 1

Answer: (D)

From lens formula, we have
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Here, $f=5cm$.
Taking the least count (error) of the measuring scale to be
$1mm=0.1cm$, for the worst case,
we get $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}+\frac{\Delta (u+v)}{u+v}$
(by using $f=\frac{uv}{u+v}$ )
Therefore,
$\frac{\Delta f}{f}=\frac{0.1}{10}+\frac{0.1}{10}+\frac{0.2}{2.0}=\frac{3}{100}$
$\Rightarrow \Delta f=\frac{3}{100}\times 5=\frac{3}{20}=0.15$
The closest answer is $f=5.00\pm 0.10cm$, that is, option (D).