Series

Caustic — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 184 mm of causticvertex radius 1.60 m, aperture 1.24 m184 mm of envelope

    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.

    part 5 · mirrors
  2. cusp — R/2 = 0.800 mvertexaperture 50 cm of a mirror of radius 1.6 mR from the cusp: 1.5996 m (0.023%)

    The caustic is the mirror's own ruler

    Four of the five instruments in this row return a ratio and refuse a size. The bright curve a mirror throws is the exception, and the reason is that it is a length lying on the table rather than an angle in a picture. Its tip is the paraxial focus, so a ruler laid from the mirror's vertex to it returns the radius of curvature — 1.5996 m against 1.6, and exactly right on a paraboloid, where there is no aberration to bias the envelope.

    part 6 · mirrors

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