Question

Calculate focal length of a spherical mirror from the following observations.

Object distance, u=(50.1±0.5)u=(50.1±0.5) cm

Image distance, v=(20.1±0.2) cm

• A. $(14.3\pm 0.4)$ cm
• B. $(14.3\pm 0.2)$ cm
• C. $(12.3\pm 0.4)$ cm
• D. $(12.3\pm 0.2)$ cm

Answer 1

The correct option is A $(14.3\pm 0.4)$ cm

Let focal length of the mirror be $f$ cm.

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

$\frac{1}{20.1}+\frac{1}{50.1}=\frac{1}{f}$ $⟹f=14.3$ cm

As, $f=\frac{uv}{u+v}$

$\therefore$ Taking log and differentiating, we get $\Delta f=f(\frac{\Delta u}{u}+\frac{\Delta v}{v}+\frac{\Delta u+\Delta v}{u+v})$

$\Delta f=14.3(\frac{0.5}{50.1}+\frac{0.2}{20.1}+\frac{0.5+0.2}{50.1+20.1})=0.4$ cm

Thus focal length of the mirror $=(14.3\pm 0.4)$ cm