Question

The graph shows relationship between object distance and image distance for an equiconvex lens. Then, focal length of the lens is

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

Answer 1

The correct option is C $5.00\pm 0.05\text{cm}$

From lens formula:

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

From the diagram we can write that,

$\frac{1}{f}=\frac{1}{10}-\frac{1}{-10}$

or $f=+5\text{cm}$

Further, $\Delta u=-0.1\text{cm}$ and $\Delta v=0.1\text{cm}$ (from the graph)

Now, differentiating the lens formula, we have

$\frac{\Delta f}{f^2}=\frac{\Delta v}{v^2}-\frac{\Delta u}{u^2}$

$\Rightarrow \Delta f=(\frac{\Delta v}{v^2}-\frac{\Delta u}{u^2})f^2$

Substituting the given data we have,

$\Delta f=(\frac{0.1}{{10}^2}-\frac{-\left(0.1\right)}{(-10{)}^2})\times (5{)}^2=0.05$

$\therefore f\pm \Delta f=5\pm 0.05\text{cm}$

Hence, option (c) is the correct answer.