OBSERVATION CHAMBER / ACTIVE

Fresnel Diffraction Observatory

Change a slit, wavelength, and screen distance. Observe near-field fringes becoming a far-field diffraction pattern.

optics / diffraction Observation Model

90 / OPTICS / FRESNEL DIFFRACTIONFIELD / Observation route

01 / OBSERVE PROPAGATION

Light spreads beyond the opening

STATIC

Focus the canvas: ← → changes distance; R resets. Green: Fresnel intensity. Dashed amber: far-field approximation, shown only when N ≤ 0.1. Phase dots are 401 discrete samples, not a resolved continuous phase curve; rapid turns between them may be missed. Phase is hidden below 10⁻⁶ of peak intensity.

Fresnel number N (full width): —
Peak I / I incident: —
Profile-window power / slit power: —
Mirror intensity error: —
max |I − I far| / N: —
Predicted far-field first null: —

02 / RECORD

Keep this diffraction state

Create a report or PNG of the current settings. Any setting change or RESET clears generated outputs.

Generated report

MODEL / BOUNDARIES

One slit under uniform illumination

Assume a monochromatic coherent plane wave, unit incident intensity, an ideal opaque screen, and a slit infinite in the vertical direction. This one-dimensional scalar Fresnel model uses the paraxial approximation in free space. It excludes polarization, material response, lenses, and evanescent fields.

The phase omits the common exp(ikz) factor. The propagation map is cropped at ±1 mm and uses log brightness. The profile changes its horizontal window with the settings; read the millimetre labels.

FORMULA / FRESNEL INTEGRAL

Add contributions across the opening

U(x,z) = e^(−iπ/4) / √(λz) · ∫[−a/2,a/2] exp(iπ(x−u)² / λz) du
I = |U|²; N = a² / (λz)
v± = √(2 / λz) (x ± a/2)
U = e^(−iπ/4) / √2 · [F(v+) − F(v−)]
F(v) = ∫[0,v] exp(iπt²/2) dt
I far = N · sinc²(πax / λz)

Here a is the full slit width, not the half width. sinc(q) = sin(q)/q. The first far-field null is predicted at x = ±λz/a. At finite N this is an approximate location, not an exact zero of the Fresnel intensity.

MIT Optics / Fresnel diffraction

HOW TO OBSERVE

From edges to a broad central lobe

Choose NEAR FIELD. Several bright ripples form near and inside the opening. The peak can exceed the incident intensity through interference.
Increase distance. N decreases and the pattern spreads. The amber line marks your screen in the propagation map.
Choose FAR FIELD. Compare the green profile with the dashed sinc² approximation. Then change wavelength or slit width and read the predicted dark-line position.

Captured power integrates only the displayed profile. Missing tails are not absorption or a conservation failure. The model conserves power on the infinite screen; this finite-window reading does not prove that identity.

NUMERICAL CHECKS

Compare independent calculations

Fresnel integrals use a fixed Simpson table with cubic interpolation below |v|=8 and a 12-term asymptotic expansion beyond it. Tests compare an independent aperture integral, known C(1) and S(1), mirror symmetry, scale invariance, near-field peaks, and the far-field limit.

The far-field error is max |I − I far| / N across 401 samples. Dividing by the predicted central intensity avoids relative-error divergence at dark fringes.

Not run

OBSERVATION POLICY

This scalar paraxial model runs in your browser. Inputs, calculations, reports, and images stay local. It does not measure light or visitors.

Route

This chamber belongs to Fields in Motion.

FIELD Back to Fields in Motion Route.