AIIMS 2018 Physics Mirror Formula MCQ Question

In this problem, we apply the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ to derive the relationship between the rates of change of image distance $v$ and object distance $u$. The derived equation $\frac{dv}{dt} = -\left(\frac{f}{u-f}\right) \frac{du}{dt}$ indicates that the rate of change of the image distance is directly proportional to the rate of change of the object distance, scaled by the factor $-\left(\frac{f}{u-f}\right)$. Given that $\frac{dv}{dt} = \frac{1}{15} \text{ m/s}$, option A correctly represents this relationship, while the other options are not applicable as they do not provide relevant information or values related to the derived equation. Understanding this relationship is crucial for analyzing how changes in object distance affect image distance in optics.