Think of it like a photocopy machine set to 100% scale: when the original document is placed at the correct calibrated focal distance from the lens, the output is an exact, life-size replica of the original.

In a convex lens, the magnification $m$ is given by the ratio of image distance $v$ to object distance $u$. When the object is at $u = -2f$, the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ results in $v = 2f$. Thus, $m = \frac{v}{u} = \frac{2f}{-2f} = -1$. The magnitude $|m| = 1$ indicates equal size, while the negative sign indicates an inverted orientation.

Always remember: If $|m| = 1$, the image distance is equal to the object distance ($|v| = |u|$). This is a hallmark of the $2f$ position for convex lenses!