magnification equation

Meaning: Magnification m compares image height to object height. Its magnitude gives size: |m| > 1 is enlarged, |m| < 1 is reduced, and |m| = 1 is the same size. Its sign gives orientation: positive is upright, negative is inverted. With the standard convention, i is positive for a real image and negative for a virtual one.

Equation: m = −i/o = hᵢ/hₒ, where m is magnification (unitless), i is image distance (m), o is object distance (m), and hᵢ and hₒ are image and object heights (m). Pair it with 1/f = 1/o + 1/i, where f is focal length (m).

On the MCAT: Given f and o for a mirror or lens, solve the lens or mirror equation for i. Then find m and state whether the image is real or virtual, upright or inverted, larger or smaller. For a system of two lenses, the total magnification is the product m₁ × m₂.

Common confusion: A negative m does not mean a smaller image. The sign gives orientation only, and size is in |m|. A plane mirror has m = +1 (upright, virtual, same size). A single diverging lens or convex mirror gives an upright, reduced, virtual image for a real object, so m is between 0 and 1.