Question

The figure shows the graph between the image distance $v$ (in cm) and the object distance $u$ (in cm) for a thin convex lens. The focal length of the lens is

• A. $(5.00\pm 0.05)cm$
• B. $(5.00\pm 0.10)cm$
• C. $(10.0\pm 0.10)cm$
• D. $(0.50\pm 0.05)cm$

Answer 1

Answer: (A)

$(5.00\pm 0.05)cm$

The formula for a convex mirror-

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

Here, we put $v=+10\text{cm}$ and $u=-10\text{cm}$-

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

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

From the graph, we can see that $\Delta u=0.1$ and $\Delta v=0.1$

Differentiating the mirror formula, we obtain-

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

$\Delta f=\left(\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}\right).f^2$

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

$\Delta f=0.05$

Therefore, the focal length of the lens is $(5\pm 0.05)\text{cm}$