Q 11-01-092JEE MainJEE Main 2024 (4 Apr, Shift 1)Medium
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
Answer: (C) $f^2\left[\dfrac{\Delta u}{u^2} + \dfrac{\Delta v}{v^2}\right]$
Lens formula: $\dfrac1f = \dfrac1v - \dfrac1u$. Differentiating and adding the magnitudes of the errors,
$$\frac{\Delta f}{f^2} = \frac{\Delta v}{v^2} + \frac{\Delta u}{u^2} \Rightarrow \Delta f = f^2\left[\frac{\Delta u}{u^2} + \frac{\Delta v}{v^2}\right]$$
Solution by Sreeraj P, M.Sc Physics