Question

If 1/f=1/u +1/v

Were u =10.5+-0.1cm and V =85+-0.1cm find minimum error in f

Answer 1

To be given in question

$u=$ 10.5 cm

$\Delta u$ =-0.1 cm

$v=$ 85 cm

$\Delta v=$ -0.1 cm 

To be asked in question

${\Delta f}=f(\frac{\Delta u}{u}+\frac{\Delta v}{v})$

We know that

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

Put value then

$f=9.3455cm$

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

${\Delta f}=f(\frac{\Delta u}{u}+\frac{\Delta v}{v})$

Put value

$\Delta f=-9.3455(\frac {-0.1}{10.5}+\frac {-0.1}{85})$

$\Delta f=-0.0999cm$