Home▸Optics & Light▸Huygens' Principle

🌊 Huygens' Principle

Interactive Huygens' Principle simulation: watch secondary wavelets form diffraction patterns through single slit, double slit, and circular apertures. Adjust wavelength, slit width and observe the far-field intensity pattern.

Optics & Light3DModerate60 FPS

About this simulation

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.

Frequently Asked Questions

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.

How is Huygens' principle used in acoustic imaging?

Medical ultrasound systems fire elements of a transducer array with carefully timed delays. Received echoes are delay-and-sum beamformed by the Huygens principle in reverse: each element's signal is time-shifted to account for the travel time from each point in the image, and the sum coherently focuses the reconstruction at that point.

What is the relationship between Huygens' principle and Fourier optics?

Fourier optics formalises Huygens–Fresnel diffraction using Fourier transforms. In the Fraunhofer limit, the diffracted field is the 2D Fourier transform of the aperture's transmission function. This powerful relationship enables design of diffractive optical elements, spatial filters, and holographic lenses using signal processing mathematics.

⚙ Under the hood

Every point on a wavefront spawns secondary wavelets — tune wavelength to watch single- and double-slit diffraction emerge from wave superposition.

Canvas 2DOpticsDiffractionHuygensWave SuperpositionDouble Slit

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install