Guide · Optical bench No.7

How LUCIDA. was made

One page, no raster images, no keyframes. Every ray is traced through real glass at runtime — the physics is the animation.

n1 sin θ1 = n2 sin θ2

The concept

The Wollaston Room is a fictional instrument-maker's bench for anyone who has ever wondered what a lens actually does to light — students, illustrators, the optically curious. The page has one job: put a working optical bench in your hands. Drag lenses, prisms, a slit and a mirror along a rail; light refracts correctly and forms — or fails to form — an image on the ground glass. Four presets rebuild the camera obscura, the camera lucida, Kepler's telescope and Newton's spectrum from the very same parts.

Palette

Argued from a blueprint under lamplight
Blueprint
#12233DThe drawing ground. Deep enough that a gold ray reads as emitted light, not ink.
Well
#0D1A2EVignette and bench frame — the dark the instrument sits in, so the rail floats.
Ray gold
#F2C063Light itself. The only warm voice on the page; every ray, focus and index dot.
Focus
#FFD98AGold at its brightest — where rays converge, and the numbers that matter.
Chalk
#DCE6F2Glass outlines and body copy, drawn as if in chalk on the blueprint. Above 8:1 contrast.
Slate
#93A9C4Annotation and quiet prose — the pencil hand beneath the chalk.

Type

STIX Two, refracted

A book face with a rigorous mathematical companion — it sets Snell's law, the plate headings and every moment of ceremony without switching fonts. The italic carries the field-note asides. Chosen because the subject is mathematics wearing glass.

Space Grotesk · ƒ220

The instrument's engraving: rail ticks, focal lengths, the live readout, every eyebrow and label. A grotesque with real character in its digits keeps the measurements legible against the moving rays.

Techniques

Signature — the ray tracer you rearrange by hand

The bench is a single Canvas 2D geometric-optics engine — no three.js, no WebGL, no library at all. The world is 1000×540 units. Each component compiles to analytic surfaces: lenses become two circular arcs (true spherical caps, so they inherit real spherical aberration), the prism and mirror become line segments, the iris a pair of stops. A fan of rays leaves the source and each is marched surface to surface, taking the nearest valid hit.

At every glass boundary the direction is bent by the vector form of Snell's law (refractDir()): with the ratio η = n₁/n₂ and the surface normal, the refracted vector is computed directly — and when η²(1−cos²θ) > 1, the law has no real solution and the ray reflects instead. That single branch is total internal reflection: the camera lucida's folding prism works because the geometry forces it, not because it was drawn that way. Colour is real too — the glass index follows a Cauchy relation n(λ) (dispersion exaggerated ~3× for legibility), so white light fans into a spectrum and violet lands short of red. A lightweight analysis pass reads the hit pattern and narrates what it sees: magnification, image sharpness, dispersion in millimetres. Nothing is keyframed; move a piece a pixel and every ray re-solves.

Second reads: set Plate II, let the folded light rest, and a pencil draws the ghost onto the paper of its own accord; close the iris in front of a lens and the image tightens as the outer zones darken — stopping down to ƒ/8 in one gesture.

Iteration log

Colophon

Designed and built in one sitting by Sapience Analytics — concept, copy, optics and the ray tracer. Part of the Generative Assets collection.

Sapience Analytics builds working instruments for real businesses — AI automation and systems that behave like physics, not slideware. Commission one.