What is the difference between Fresnel and Fraunhofer diffraction?

Fresnel diffraction applies in the near field, where the curvature of wavefronts matters and the pattern changes with distance. Fraunhofer diffraction applies far from the aperture (or in the focal plane of a lens), where the pattern is effectively the Fourier transform of the aperture function and does not change shape with distance.

How does a double-slit relate to Huygens' principle?

Each slit acts as a set of Huygens secondary sources. Light from the two slits propagates and interferes, creating the alternating bright and dark fringes of Young's double-slit pattern. Huygens' principle correctly predicts fringe spacing as λL/d, where L is the screen distance and d is the slit separation.

What is the Fresnel number and why does it matter?

The Fresnel number F = a²/(λL) characterises the diffraction regime. F >> 1 indicates Fresnel (near-field) diffraction; F << 1 indicates Fraunhofer (far-field) diffraction. It determines whether a focusing element is needed to observe far-field patterns at a manageable distance.

🌀 Huygens' Principle & Wave Diffraction

Every point on a wavefront is a source of secondary spherical wavelets. Their superposition forms the next wavefront — and when a barrier interrupts them, diffraction occurs. Adjust wavelength, slit width, and preset to see single-slit, double-slit (Young's experiment) and circular aperture patterns. Click the canvas to add point sources.

Preset

Parameters

Wavelength λ 550 nm

Slit width 3.0 λ

Slit separation 8.0 λ

Wave speed 1.0×

Source density 12

Stats

Wavelength λ550 nm

Slit width / λ3.00

Central max θ—

1st min θ19.47°

ModeSingle Slit

Huygens' Principle

Proposed by Christiaan Huygens in 1678: every point on a propagating wavefront acts as a point source of secondary spherical wavelets. The new wavefront is the envelope of all those wavelets. When part of the wavefront is blocked by a barrier with an aperture, the remaining secondary sources radiate into the geometric shadow — producing diffraction.

Single-Slit Diffraction

A slit of width a diffracts light so that the intensity minima occur at angles where an integer number of half-wavelengths fit across the slit:

Minima: a · sinθ = mλ (m = ±1, ±2, …)
Intensity: I(θ) = I₀ · sinc²(β/2), where β = (πa sinθ) / λ
Central maximum half-width: θ₁ = arcsin(λ/a)

Double-Slit (Young's Experiment)

Two slits separated by distance d produce bright fringes (constructive interference) where the path difference is an integer multiple of λ:

Bright fringes: d · sinθ = mλ (m = 0, ±1, ±2, …)
Dark fringes: d · sinθ = (m + ½)λ
Fringe spacing (small θ): ∆y = λL / d

Applications

CD/DVD grooves act as diffraction gratings — the groove spacing (~1.6 µm) is comparable to visible-light wavelengths, separating colours. X-ray crystallography (Bragg diffraction) uses the periodic atomic lattice as a 3D grating to determine crystal structure. Radio telescopes use aperture synthesis to overcome single-dish diffraction limits. Even the human iris sets a limit on visual acuity through diffraction (Rayleigh criterion: θ ≈ 1.22 λ/D).

About this simulation

Last updated: 5 July 2026

This page turns Huygens' construction into a full 2-D wave field: every open point of the aperture emits a secondary spherical wavelet, and the canvas on the left renders the true, colour-coded sum of all those wavelets pixel by pixel. The graph on the right shows the analytic far-field intensity for the current preset — single slit, double slit, a circular aperture, or freely placed point sources — computed from the sinc-squared and Airy-disc formulas given below the canvas.

🔬 What it shows

A live wave field to the left of the barrier, and a scrolling far-field intensity curve to the right, both driven by the same aperture. In Single Slit and Double Slit presets the curve follows the sinc²(β/2) diffraction envelope (plus an interference factor for two slits); Circular gives the Airy-disc pattern with its first dark ring at θ ≈ 1.22λ/D; Point Sources sums whatever sources you have placed by clicking the canvas.

🎮 How to use

Pick a preset with the four buttons (Single Slit, Double Slit, Circular, Point Sources), then drag Wavelength λ to see the true visible colour and pattern spacing change, Slit width and Slit separation to reshape the fringes, Wave speed to speed up or slow the animation, and Source density to control how finely the aperture is sampled into Huygens sources. In Point Sources mode, click anywhere on the wave canvas to drop your own source and watch the intensity graph update instantly.

💡 Did you know?

The Fresnel number a²/(λL) tells you whether a given aperture and distance sit in the near-field (Fresnel) or far-field (Fraunhofer) regime shown on this page. The same aperture-summation idea used here also underlies X-ray crystallography, radio-telescope aperture synthesis, and the diffraction-limited resolution of your own eye's pupil.

Frequently asked questions

What is the difference between the four presets?

Single Slit places Huygens sources evenly across one gap of adjustable width; Double Slit splits that same source budget between two gaps separated by the Slit separation slider, adding path-difference interference on top of each slit's own diffraction; Circular arranges sources around a ring to approximate a round aperture, producing Airy-disc rings instead of straight fringes; Point Sources ignores the aperture entirely and instead sums whatever individual sources you place by clicking the canvas.

How is the far-field intensity graph on the right actually computed?

For Single Slit it evaluates the standard sinc²(β/2) diffraction formula; for Double Slit it multiplies that same envelope by a cos²(δ) interference factor from the two-slit path difference; for Circular it uses an Airy-disc approximation built from a Bessel-like J1(u)/u term; for Point Sources it coherently sums the phase kr·sinθ from every placed source at each output angle, which is exactly Huygens' summation performed analytically instead of pixel by pixel.

What does the Wavelength slider actually change?

Dragging it between 380 and 700 nanometres updates the colour swatch to the true visible colour at that wavelength, rescales the pixel-space wavelength used inside the wave-field renderer, and shifts every fringe and ring in the far-field graph, since diffraction angles scale directly with λ.

What does Source density control, and why would I change it?

It sets how many individual Huygens point sources are sampled across the open aperture (from 4 up to 32). Too few sources make the wave field look blocky and can distort the pattern at wide angles; more sources give a smoother, more physically faithful approximation to the true continuous wavefront, at some cost to frame rate.

What happens if I place several point sources close together in Point Sources mode?

Each click adds one more coherent emitter to the sum used by both the wave-field renderer and the far-field graph. Two nearby sources behave like a miniature double slit, producing broad interference fringes; several sources arranged in a line or curve start to approximate a custom-shaped aperture or even a simple diffraction grating, all built up from the same Huygens summation.

About Huygens' Principle Wave Demo

The Huygens–Fresnel principle provides a powerful method for computing the propagation of waves through complex apertures and obstacles. At its heart is the idea that any wavefront can be decomposed into infinitely many point sources of spherical secondary waves, and the subsequent field is determined by their coherent superposition. This turns wave propagation into an integration problem solvable by Fourier methods.

In practice, the simulation discretises the wavefront into point sources arranged on a grid. Each source emits a spherical wave with amplitude decreasing as 1/r and phase accumulating as kr = 2πr/λ. Summing contributions at each observation point reproduces diffraction rings, interference fringes, and focal spots with high fidelity. The near-field (Fresnel) and far-field (Fraunhofer) regimes produce qualitatively different patterns.

Engineering applications of the Huygens–Fresnel principle span antenna array synthesis, acoustic beam-forming in sonar and medical ultrasound, digital holographic reconstruction, and optical lithography for semiconductor chip manufacturing. In lithography, controlling the interference of thousands of secondary wavelet sources allows patterns to be printed with features smaller than the wavelength of light.