In an experiment to measure the focal length $(f)$ of a convex lens,the least counts of the measuring scales for the position of the object $(u)$ and for the position of the image $(v)$ are $\Delta u$ and $\Delta v$,respectively. The error in the measurement of the focal length of the convex lens will be:

• A
  $\frac{\Delta u}{u} + \frac{\Delta v}{v}$
• B
  $f^2 \left[ \frac{\Delta u}{u^2} + \frac{\Delta v}{v^2} \right]$
• C
  $2f \left[ \frac{\Delta u}{u} + \frac{\Delta v}{v} \right]$
• D
  $f \left[ \frac{\Delta u}{u} + \frac{\Delta v}{v} \right]$