QJEEM24Phb767: JEE Main 2024 Physics - Class 12 JEEM24Phb767 Solution: In an experiment to measure focal length ( ) of convex lens,…

First, let's understand the relationship between the object distance ( $u$ ), the image distance ( $v$ ), and the focal length ( $f$ ) of a convex lens, which is given by the lens formula:

Now, to find the error in the focal length ( $\Delta f$ ) due to the errors in the measurements of $u$ and $v$ ( $\Delta u$ and $\Delta v$ , respectively), we have to differentiate the lens formula with respect to $u$ and $v$ , keeping in mind the propagation of error.

By differentiating both sides of the lens formula with respect to $v$ and $u$ , and also considering the negative reciprocal relation (given $f$ is a constant for a specific lens), we have:

Rearranging this equation to find $\Delta f$ , we get:

Therefore, the correct option showing the error in the measurement of the focal length of the convex lens, taking into account the least counts ( $\Delta u$ and $\Delta v$ ) of the measuring scales for the position of the object ( $u$ ) and for the position of the image ( $v$ ), is:

Option C: $f^2\left[\frac{\Delta \mathrm{u}}{\mathrm{u}^2}+\frac{\Delta \mathrm{v}}{\mathrm{v}^2}\right]$