Physics - Geometrical Optics Question with Solution | TestHub

The formula for a lens is given by $\frac{1}{f}=\frac{1}{v}-\frac{1}{u} ...\left(i\right)$

$u=\left(100\pm 0.2\right) \mathrm{cm}-\left(80\pm 0.2\right) \mathrm{cm}=\left(20\pm 0.4\right) \mathrm{cm}$

$v=\left(180\pm 0.2\right) \mathrm{cm}-\left(100\pm 0.2\right) \mathrm{cm}=\left(80\pm 0.4\right) \mathrm{cm}$

Substituting the values in the equation of focal length,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=\frac{1}{80}-\left(-\frac{1}{20}\right)=\frac{5}{80}$

$\Rightarrow f=16 \mathrm{cm}$

Differentiating the equation (i)

$\frac{df}{f^2}=\frac{dv}{v^2}+\frac{du}{u^2}$(Only positive sign is considered for error calculation)

$=\frac{0.4}{6400}+\frac{0.4}{400}=0.4\times \frac{17}{6400}$

$\Rightarrow df=0.4\times \frac{17}{6400}\times {16}^2=0.272$

The percentage error is 

$\frac{df}{f}\times 100=\frac{0.272}{16}\times 100=1.70\%$