Huygens' Principle
Wavelets build next wavefront.
A flat ocean wavefront approaches a seawall with a narrow opening. According to Huygens, every point on a wavefront acts as a source of new spherical wavelets.
How does a flat wavefront stay flat as it propagates through open space?
The envelope does the magic! Every point on the wavefront emits a spherical wavelet. After a tiny time dt, each wavelet has expanded by c·dt. Draw the forward tangent surface to ALL these little spheres — it’s a new flat plane, displaced forward by c·dt. The wavelets going backward cancel out. Huygens’ construction perfectly reproduces straight-line propagation, reflection, refraction, AND diffraction — all from one simple principle.
Loading simulation…
Watch wavelets expand from every point on the wavefront. See how their envelope reconstructs the next wavefront. Try a gap in a barrier: the limited number of wavelet sources there creates a curved wavefront — that’s diffraction!
New wavefront = envelope of all wavelets at r = vΔt
One construction, four phenomena. Huygens showed that propagation, reflection, refraction, and diffraction are all manifestations of the same wavelet principle. Change the geometry, and the envelope gives you the answer.
Ocean waves entering a narrow harbor opening spread into the harbor’s shadow zone. Only a few wavelet sources exist at the gap, so the envelope is curved — the wave diffracts around corners. Huygens explains it instantly.
A lens works by making wavelet travel times equal for all paths from object to image. The curved glass surface gives longer paths through slower glass, equalizing the total phase. Huygens’ principle is the foundation of geometric optics.
You can hear someone around a corner because sound wavelengths are comparable to doorway sizes. The wavelet sources at the door opening create a curved wavefront that spreads into the room.
Geophysicists use Huygens’ principle to model earthquake wave propagation through Earth’s layered interior. Each subsurface interface generates new wavelets, predicting reflections and refractions.
“Every point on a wave is a tiny broadcaster. The collective envelope of all those broadcasts IS the next wavefront. One principle to rule them all.”
Huygens’ Construction Lab
Build wavefronts from wavelets. Watch the envelope construction in action for flat waves, curved waves, refraction at interfaces, and diffraction through openings.
Loading simulation…
Start with a flat wavefront in open space. Watch the wavelets expand and form a new flat front. Now add a barrier with a narrow gap — the wavelets that make it through create a curved front, showing diffraction. Try a boundary between two media with different speeds — smaller wavelet radii in the slower medium tilt the front, demonstrating Snell’s law geometrically. Use a concave mirror to see how the envelope converges to a focal point!
Huygens’ principle is a universal wavefront propagator. Whether the wave is straight, curved, reflecting, refracting, or diffracting, the envelope of secondary wavelets gives you the answer. It’s the geometric heart of all wave optics.