AIIMS 2018 Physics Mirror Formula MCQ Question

Option B is correct because the derivation presented in the question contains an error in the sign convention for the radius of curvature $R$ and the object distance $u$. In the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{2}{R}$, the object distance $u$ should be considered negative for real objects, leading to inconsistencies in the derived equation $v = \frac{RU}{R - 2U}$. Other options are not applicable as they do not provide a valid interpretation or correction of the derivation, reinforcing the importance of adhering to proper sign conventions in optics.