Calculate the focal length of a spherical mirror form the following calculations, $\mathrm{u}=(50.0\pm 0.5)\mathrm{cm}\text{ and }\mathrm{V}=(20.0\pm 0.2)\mathrm{cm},$ $\left(\text{ Given }\frac{1}{\mathrm{f}}=\frac{1}{ \mathrm{V}}+\frac{1}{\mathrm{u}}\right)$

Calculate the focal length

$$\begin{gathered} \mathrm{f}=\frac{\mathrm{uv}}{(\mathrm{u}+\mathrm{v})}=\frac{50\times 20}{70}=14.3 \mathrm{cm} \\ \frac{\mathrm{\Delta f}}{\mathrm{f}}=\frac{\mathrm{\Delta u}}{\mathrm{u}}+\frac{\mathrm{\Delta v}}{\mathrm{v}}+\frac{\mathrm{\Delta }(\mathrm{u}+\mathrm{v})}{\mathrm{u}+\mathrm{v}} \\ \frac{\mathrm{\Delta f}}{14.3}=\frac{0.5}{50}+\frac{0.2}{20}+\frac{0.7}{70} \\ \mathrm{\Delta f}=14.\times 3\frac{3}{100}=0.429 \\ \therefore \mathrm{f}=(14.3\pm 0.429) \mathrm{cm} \end{gathered}$$