Answer:
As \[\frac{1}{f}=\frac{1}{u}=\frac{1}{v}=\frac{v+u}{uv}\]
\[f=\frac{uv}{u+v}=\frac{(50.1)(20.1)}{(50.1+20.1)}=\text{
14}.\text{3 cm}\]
.
From \[\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\]
\[\frac{-\Delta
f}{{{f}^{2}}}=\frac{-\Delta u}{u}-\frac{\Delta v}{{{v}^{2}}}\]
\[\Delta \text{f }=\Delta \text{u}{{\left(
\frac{f}{u} \right)}^{2}}+\Delta \upsilon {{\left( \frac{f}{\upsilon }
\right)}^{2}}=0.5{{\left( \frac{14.3}{20.1} \right)}^{2}}=0.04+0.10=0.14cm\]
\[\text{f
}=\left( \text{14}.\text{3 }\pm 0.\text{1} \right)\text{ cm}\]
.
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