Question

The focal length of a mirror is given by $\frac{1}{f}=\frac{1}{u}+\frac{1 \, }{v}$ where $u$ and $v$ represent object and image distances respectively. The maximum relative error in $f$ is

• A. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}$
• B. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}-\frac{\Delta \left(u + v\right)}{u + v}$
• C. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}-\frac{\Delta \left(u - v\right)}{u + v}$
• D. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}+\frac{\Delta u}{u + v}+\frac{\Delta v}{u + v}$

Answer 1

Answer: (D)

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