Question

Focal length of a concave mirror is given by
1/f= 1/v+1/u
where u = (-20 plus minus 0.5)
v = (30 plus minus 0.1)
Calculate focal length with error limits

Answer 1

Dear Student
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u}andv=30cmandlimits0.1andu=-20cmwithlimits0.5cm \\ \frac{1}{f}=\frac{1}{30}-\frac{1}{20}=\frac{-1}{60} \\ f=-60cm \\ soforlimits \\ f=\frac{v\times u}{v+u} \\ f=errorinv+errorinu/errorinv+errorinu \\ f=0.6/0.6=0.6+0.6=1.2cm \\ sofocallenghthis-60cmwitherrorlimitsof1.2cm \end{gathered}$$