magnification

Meaning: Magnification compares the size of an image with the size of the object. It is a unitless ratio that follows from similar triangles at a mirror or lens, which is why image height over object height equals −i/o. The sign shows orientation: negative m means an inverted image, positive m means an upright one. The magnitude shows size: |m| > 1 is enlarged, |m| < 1 is reduced, and |m| = 1 is the same size.

Equation: m = hi/ho = −i/o, where hi is image height (m), ho is object height (m), i is image distance (m), and o is object distance (m). The quantity m has no unit. By the usual convention, i is positive for a real image and negative for a virtual image.

On the MCAT: A question gives f and o. You find i from 1/f = 1/o + 1/i, then find m. A common prediction is that an object beyond 2f of a converging lens gives a real, inverted, reduced image, while an object inside f gives a virtual, upright, enlarged image. In a compound microscope, the total magnification is the product of the objective and eyepiece magnifications.

Common confusion: A negative m does not mean a smaller image. It means an inverted one, and size comes only from |m|. A plane mirror has m = +1, so its image is virtual, upright and the same size.