A concave mirror is a polished slice of a sphere, and that sphere has a radius $R$ — the radius of curvature. Shine parallel rays at the mirror (sunlight does nicely) and they all bounce through one bright point: the focus. The distance from the mirror out to that point is the focal length $f$ — both $f$ and $R$ are lengths, in centimetres on this paper. The geometry lands somewhere memorable: $f = \dfrac{R}{2}$ — read aloud: f equals R over two). The focus sits exactly HALFWAY between the mirror and the centre of its sphere. That's the entire formula — this chapter's gentlest.

You own one: the back of a spoon is a convex mirror (tiny, right-side-up you), and the bowl is concave — hold it close and you're magnified; back away past the focus and you flip upside down. Shaving and makeup mirrors are ground to put your face inside the focal length on purpose. Same law runs telescope mirrors the size of rooms.