THE DIFFRACTION GRATING.

Thousands of slits turn a beam into a spectrum. Where two slits whisper, ten thousand shout — the maxima grow razor-sharp and each wavelength is sent to its own angle. This is the ruler of light: d·sinθ = mλ, and longer waves bend more, the opposite of a prism.

source Fraunhofer, “Neue Modifikation des Lichtes…”, Denkschr. k. Akad. Wiss. München 8 (1821–22, pub. 1824), pp. 3–76 — no stable open link; cited author/title/year. Rendered, not quoted.

Blue Team · builds & defends

3 THE MODEL

A grating is N equally spaced slits, pitch d. Waves from all slits add in phase only when the path difference between neighbours is a whole number of wavelengths:

d·sinθ = mλ  (m = 0, ±1, ±2 …)

The N-slit amplitude is a ratio of sines; its principal peaks reach N² in intensity and narrow as 1/N. Dispersion (angle per wavelength) is dθ/dλ = m/(d·cosθ) > 0.

5 THE LINEAGE

Two slits give a soft cosine fringe (the-double-slit, Young 1804). Add more slits and the fringes sharpen into lines; at Fraunhofer's 260 wires they became a spectrum. The grating is the many-slit limit of the double slit, and the finer ruler that the-dispersion (a prism) can only sketch — but with the sign of bending reversed.

7 THE WITNESS

A live re-check of the engine: it re-derives the first-order angles for red and blue and confirms red bends further (real dispersion). If window 6 drops the λ term, the two angles collapse and this badge flips.

re-checking…

▼ the machine ▼

4 DATA IN in ↓

grating pitch d lines / mm slits N λ range400–700 nm (visible)
▼ ▼ ▼

0 THE PANEL lit

Live grating: each visible wavelength sent to θ=arcsin(mλ/d) for every order that fits.

violet 420 cyan 490 green 540 yellow 580 red 680
orders visible (each side) θ₁ green (m=1) dθ/dλ (m=1, green) resolving power R=mN (m=1)
▼ ▼ ▼

8 DATA OUT out ↓

A proven spectrum: red is thrown wider than blue in every order; peaks are 1/N thin; orders can overlap for a broad source.

booting…

Red Team · attacks & breaks

1 THE ADVERSARY wall

“Slits just cast shadows — more slits, more shadows, no colour.” The wall: geometric shadow-casting predicts no wavelength sorting. Only wave interference, adding N phasors, forces each λ to a distinct angle with peaks that sharpen as N grows. Ray optics cannot make a spectrum; the equation d·sinθ=mλ is unavoidably wave.

2 THE GRAVEYARD

“A grating bends red less than blue, like a prism.”
→ Opposite. dθ/dλ = m/(d cosθ) > 0, so longer λ bends more. Prism dispersion is normal (blue more); grating dispersion is reversed.

“You always see infinitely many orders.”
→ Bounded by |m| ≤ d/λ. Beyond it sinθ>1 — no solution.

“More slits move the lines.”
→ They don't move the peaks; they narrow them (~1/N) and raise resolving power R=mN.

6 THE TAMPER

The disclosed planted void: replace mλ with a constant — drop the wavelength. All colours then map to one angle and the spectrum dies. The Witness (7) catches it live.