Two beams overlap into bright and dark bands. Where the two paths differ by a whole wavelength the crests stack and the screen is bright; where they differ by half a wavelength crest meets trough and the screen is dark. That comb of fringes is the experiment that proved light a wave. Rendered, not quoted.
source Young, T. (1804), The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics, Phil. Trans. R. Soc. Lond. 94, 1–16 — doi:10.1098/rstl.1804.0001
Two slits, separation d, lit coherently. A point on a distant screen sits at angle θ. The upper and lower paths differ by Δ = d·sinθ.
Bright where the paths agree by a whole wavelength: d·sinθ = m·λ (m = 0, ±1, ±2 …). Dark at the half‑steps: d·sinθ = (m+½)λ.
Amplitudes add, so the intensity is I = I₀·cos²(πd·sinθ/λ). On a screen at distance L the small‑angle fringe spacing is Δy = λL/d.
Two beams make bands — Young, 1804. The same law d·sinθ = mλ with spacing λL/d and a cos² envelope is the two‑slit seed of the‑diffraction‑grating: add more slits and each bright order sharpens into a spectral line. One interference; many apertures.
Live re‑check: recomputes the peak, the null, the three spacing dependencies and the 4× centre doubling from the pure engine, then re‑runs them with the tamper armed to confirm it is caught.
re‑checking…Wavelength λ, slit separation d, screen distance L. Drag them.
Top strip: the fringes as the screen sees them. Curve: I(θ) = I₀cos²(πd·sinθ/λ) — the live engine, no baked pixels.
Proven result: a bright central fringe with equal‑width copies flanking it, spacing Δy = λL/d, centre four times a single slit. Two slits → a wave.
…“Bands could be the slits casting shadows, not waves adding.” The wall: shadow edges do not move when you change λ, but the fringe spacing Δy = λL/d scales with colour — red fringes wider than blue, from the same slits. And close one slit: the bands vanish entirely. A shadow theory predicts neither.
“Two slits give twice one slit’s brightness.” → at the centre amplitudes add before squaring, so I = (2a)² = 4× a single slit — energy re‑dealt, not created (dark fringes pay for bright).
“Fringes only need one beam.” → block either slit and the cos² modulation dies; interference needs two coherent paths.
“Bigger d spreads the pattern out.” → opposite: Δy = λL/d shrinks as d grows.
The disclosed planted void: swap maxima and minima — put the bright fringes at the half‑integer path differences (cos² → sin²). The pattern inverts; the “bright at whole‑λ” law fails. The Witness (7) catches it live.