The Mirror Equation and Magnification

A curved mirror bends every ray that hits it according to the same rule, so instead of tracing three rays by hand every time, you can solve one equation. The mirror equation, 1/do + 1/di = 1/f, packs the whole geometry of reflection into a single relationship among object distance do, image distance di, and focal length f. Once you know di, the magnification m = -di/do tells you how big the image is compared to the object and whether it's flipped. A magnitude greater than 1 means enlarged, less than 1 means shrunk, and the sign tells you upright or inverted.

The sign convention is what keeps the equation truthful instead of ambiguous. Distances measured on the side where light actually travels after reflecting (in front of the mirror) count as positive; distances behind the mirror, where light only appears to come from, count as negative. f is positive for concave mirrors and negative for convex ones. Follow those rules and the algebra automatically tells you whether an image is real or virtual, upright or inverted, without you having to guess from a sketch.

This topic is the algebraic twin of ray tracing: ray diagrams show you why the equation works, and the equation lets you get exact numbers fast. It also sets up refraction at lenses, where the same equation reappears with di and do swapped across the lens instead of the mirror, and the same magnification formula still applies.