An object placed $40\text{ cm}$ in front of a thin convex lens is moved to $60\text{ cm}$ from the lens. If the focal length of the lens is $30\text{ cm}$, the ratio of magnification of the image at the initial position to the final position is:
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Using the $m = \frac{f}{f+u}$ formula avoids the multi-step process of finding the image position $v$ first via $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$, saving valuable time during exams.