Fresnel straight-edge diffraction

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?

▶ Run the simulationSee the measured result

Units: dimensionless intensity ratio I(edge)/I₀ at the geometrical shadow edge of a straight edge

How the lab tests it

Grazing 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.

What it checks

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.

Fresnel diffraction, Fresnel number & knife-edge calculator

The edge of a shadow is not an edge. Run a straight edge across a beam and the light does not stop at the geometric boundary: it overshoots to 1.37 times the incident intensity just inside the lit side, rings down through a decaying fringe train, leaks smoothly into the geometric shadow, and at the boundary itself sits at exactly one quarter — a number no ray or corpuscle picture can produce, and the reason Fresnel's 1818 memoir won the Académie's prize over Poisson's objection. This calculator computes all of it from one declared primitive: the phase exp(iπt²/2) a secondary wavelet carries, integrated over the open half of the wavefront. Nothing it is about is stored. The endpoint one-half never appears in the code — U(0) comes back from the quadrature and misses a typed half by about 9e-16, which the page prints rather than hides — and the quarter is then the mirror symmetry doing arithmetic: the free wavefront is twice U(0), so the ratio is a division by four that floating point returns exactly, at every wavelength and every screen distance. The two extrema are located by bracket-and-refine on the computed curve, with no tabulated position seeded, and the textbook 1.3704 at w = 1.2172 and 0.7783 at 1.8725 are loaded only to be scored against them. The screen's amplitude transmission τ is a real dial rather than a decoration: at τ = 0 the edge is opaque and reads a quarter, at τ = 1 there is no screen and it reads exactly 1, at τ = −1 a phase-reversing plate makes the edge exactly black — one parameter carrying the whole trichotomy, and a stored quarter would return a quarter at all three. The same integral is what a radio path is planned with, so it is offered in those units too: the first Fresnel zone radius, the obstruction parameter ν, and the diffraction loss in decibels, where a knife edge grazing the line of sight costs 6.02 dB — which is this page's quarter, written logarithmically. Four things it will NOT do. It does not attempt Sommerfeld's exact vector half-plane solution, which departs from this scalar paraxial integral within about a wavelength of the edge and is what neither the simulation above nor its oracle computes. It does not model a real edge's thickness, conductivity or roughness. For a radio path it is a single knife edge only — no ground reflection, no second edge, no rounded-obstacle correction, no atmospheric refraction, no terrain. And it does not correct the simulation above: the screen displays 1.380 where the continuum answer is 1.3704429, and this page prices that gap against the three systematics the finding discloses rather than editing either number to agree.