Straight-edge shadows look sharp — but if light is a wave, what happens right at the edge of the shadow, and can a ray picture survive a close look?
▶ Launch the interactive simulationGrazing a plane wave past an opaque half-plane, superpose Huygens secondary wavelets over the open half onto a screen at distance L — cylindrical wavelets K(χ)·e^{ikr}/√r with the exact Fresnel phase k(y−x)²/(2L), no Cornu-spiral formula and no ¼ coded. Read the intensity at the geometric shadow edge, the first-fringe overshoot and dip, the light that leaks into the shadow, and sweep λ and L to test the fringe scaling.
the intensity at the geometrical shadow edge is exactly I₀/4 — the open half of the wavefront contributes exactly HALF the unobstructed amplitude (mirror symmetry), so a quarter of the intensity — recovered here to 1e-8 from the raw phasor sum, never hand-fed. The lit side does NOT settle straight to I₀: it OVERSHOOTS to ≈1.37 I₀ at the first bright fringe (w≈1.22) and dips to ≈0.78 I₀ (w≈1.87), ringing down with decaying fringes; a ray/corpuscular picture can never exceed the incident intensity, so the 37% overshoot alone falsifies geometric optics, and light also LEAKS smoothly into the geometric shadow (no sharp edge). Fringe positions scale as √(λL) — the near-field (Fresnel) signature, distinct from the far-field linear-in-λ scaling of ?world=young / ?world=grating / ?world=airy. This is exactly Poisson's 'absurd' consequence — a bright spot at the very centre of a disk's shadow — that Arago observed in 1818, winning the Académie prize for the wave theory over Newton's corpuscles. The near-field opening of the lab's Fraunhofer diffraction arc.