Question

The graph between object distance $u$ and image distance $v$ from a convex lens is given. The correct option option, from the following, is

• A. $f=5\pm 0\cdot 1$
• B. $f=5\pm 0\cdot 05$
• C. $f=0\cdot 5\pm 0\cdot 1$
• D. $f=0\cdot 5\pm 0\cdot 05$

Answer 1

Answer: (B)

From the lens formula :
We have $\frac{1}{\text{f}}=\frac{1}{\upsilon }-\frac{1}{\text{u}}$
$\frac{1}{\text{f}}=\frac{1}{10}-\frac{1}{-10}$
or, $\text{f}=+5$
Further, $\Delta \text{u}=0\cdot 1$
and $\Delta \upsilon =0\cdot 1$ ( from the graph )
Now, differentiating the lens formula, we have
$\frac{\Delta \text{f}}{{\text{f}}^2}=\frac{\Delta \upsilon }{{\upsilon }^2}+\frac{\Delta \text{u}}{{\text{u}}^2}$
or, $\Delta f=\left(\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}\right)f^2$
Substituting the values, we get
$\Delta \text{f}=\left(\frac{0\cdot 1}{10^2}+\frac{0\cdot 1}{10^2}\right){\left(5\right)}^2=0\cdot 05$

$\therefore \text{f}\pm \Delta \text{f}=5\pm 0\cdot 05$