THE DISPERSION

Glass bends blue more than red, so a prism unfolds white light into a rainbow. The refractive index falls with wavelength — n(λ)=A+B/λ² — the short blue waves see a higher index and turn hardest. Rendered, not quoted.

source Newton, Opticks (1704), prism dispersion of white light  ·  Cauchy, Mémoire sur la Dispersion de la Lumière (Prague, 1836); reported Comptes Rendus Acad. Sci. 2, 341 (1836) — no stable per-memoir DOI · cite author/title/year amber

Blue Team · builds & defends
3

The Model

Cauchy's empirical law for a transparent medium: n(λ)=A+B/λ² with B>0. Because the term B/λ² shrinks as λ grows, n decreases with wavelength (normal dispersion).

Short-λ blue therefore sees a higher index than long-λ red and — by Snell at each prism face — deviates more. The angular spread is set by dn/dλ = −2B/λ³ < 0.

Constants used: A=1.5046, B=4200 nm² (crown-glass fit).

5

The Lineage

White light unfolds — Newton 1704 proved the prism separates rather than dyes; Cauchy 1836 gave the falling n(λ).

This is the refraction of the-snell-law made colour-dependent. And it runs opposite to the-diffraction-grating: a grating's d·sinθ = m·λ throws long wavelengths farthest (red outermost), while a prism throws short ones farthest (blue outermost). Same rainbow, mirrored order.

7

The Witness live

Re-checks the live engine every render: does nblue > nred and dn/dλ<0 still hold? If the Tamper (6) flips B negative, this flag goes red.

witness pending…
The Machine
4

Data In in ▼

white light band400 – 700 nm
sample lines F / D / C486 · 589 · 656 nm
prism apex angle60°
incidence at face 150°
glass fit A, B1.5046 · 4200 nm²
SNELL AT EACH FACE
0

The Panel LIT

index curve n(λ) top-left · white ray splits at the prism · blue green red
PROVEN RESULT
8

Data Out out ▼

Blue's index exceeds red's, so blue deviates more and the spectrum spreads with violet on the inside of the prism's bend — the opposite hand to a grating.

booting…
Red Team · attacks & breaks
1

The Adversary WALL

Cauchy's law is empirical, not universal. It only holds in a material's transparent window. Near an absorption band the medium shows anomalous dispersion: n can rise with λ and dn/dλ>0 — there red really can bend more.

So "blue always bends more" is a claim about normal dispersion only. Push λ into the UV/IR resonances and the two-term fit breaks; you need Sellmeier's resonant form.

2

The Graveyard

A prism colours white light by staining it.
→ It separates colours already present (Newton 1704).

Glass bends every colour by the same angle.
→ n depends on λ; blue turns ~0.7° more than red here.

Red bends more than blue in a prism.
→ Only under anomalous dispersion; in normal glass blue bends more.

Prism and grating give the same colour order.
→ Opposite: grating throws long-λ farthest, prism throws short-λ farthest.

6

The Tamper

The disclosed planted void: flip B<0 so n rises with λ. Red would bend more, the rainbow order inverts, and the Witness (7) must catch it live.