Aperture — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as cusp, envelope, focus, paraboloid, spherical aberration — the same set of essays touches all of them, so they are one junction rather than several.
Where the focus went
If the reflected rays do not meet at a point, they meet each other in pairs, and the curve they are all tangent to is what the mirror has instead of a focus. On a sphere of 1.6 m vertex radius it is 184.1 mm long and has a cusp; near the axis it sits at R/2, which is why a small enough spherical mirror passes for a good one. This is the bright shape in the bottom of a coffee cup, computed rather than admired.
The one shape that focuses
A paraboloid takes every ray parallel to its axis exactly through one point — 4.8e-9 mm of envelope across a 1.24 m aperture, which is arithmetic. A sphere with the same vertex curvature spreads the same bundle over 184.1 mm. So there is exactly one curved mirror that is a projection through a centre, it is a projection for exactly one bundle of rays, and every telescope in the world is built out of that sentence.
Named alongside it
The objects these essays reach for when they reach for this one.
Causticcentre of projectionCuspEnvelopeFocusParaboloidRay tracingReflectionSpherical aberrationAstigmatismConicNot a projection