focal length

Meaning: Focal length (f) is the distance from a mirror or thin lens to its focal point, where rays parallel to the principal axis converge, or from which they appear to diverge. A shorter f means stronger bending of light. For a spherical mirror, f = R/2. Concave mirrors and converging (convex) lenses have positive f; convex mirrors and diverging (concave) lenses have negative f.

Equation: 1/f = 1/o + 1/i, where f is focal length (m), o is object distance (m), and i is image distance (m). For mirrors, f = R/2, with R the radius of curvature (m). Lens power P = 1/f, in diopters (m⁻¹).

On the MCAT: Given o and f, solve for i, then use magnification m = −i/o (dimensionless) to classify the image. With a converging element, an object beyond f gives a real, inverted image; an object inside f gives a virtual, upright, enlarged image. Thin lenses in contact have powers that add. Eye, microscope and telescope questions use the same equation.

Common confusion: Focal length is not the image distance. The image lies at the focal point only when the object is very far away (o → ∞). Keep signs straight: diverging elements have negative f, and virtual images have negative i.