Q. 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) $\frac{\mathrm{\Delta}f}{f} = \frac{\mathrm{\Delta}u}{u} + \frac{\mathrm{\Delta}v}{v}$
B) $\frac{\mathrm{\Delta}f}{f} = \frac{1}{\mathrm{\Delta}u/u} + \frac{1}{\mathrm{\Delta}v/v}$
C) $\frac{\mathrm{\Delta}f}{f} = \frac{\mathrm{\Delta}u}{u} + \frac{\mathrm{\Delta}v}{v} - \frac{\mathrm{\Delta}(u + v)}{u + v}$
D) $\frac{\mathrm{\Delta}f}{f} = \frac{\mathrm{\Delta}u}{u} + \frac{\mathrm{\Delta}v}{v} + \frac{\mathrm{\Delta}u}{u + v} + \frac{\mathrm{\Delta}v}{u + v}$
Explanation
$f = \frac{uv}{u + v},\frac{\mathrm{\Delta}f}{f} = \frac{\mathrm{\Delta}u}{u} + \frac{\mathrm{\Delta}v}{v} + \frac{(u + v)}{u + v}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.