★★ Intermediate

🌊 Huygens' Principle

Every point on a wavefront acts as a new point source of secondary spherical wavelets. The new wavefront is the envelope of all these wavelets — explaining diffraction, refraction, and interference from first principles.

Wavelength λ = 40 px Slit width a = 60 px Slit sep. d = 140 px Speed = 1.0×

λ = 40 px Slit width / λ = 1.50 1st min θ = —° Mode: Plane Wave

Huygens–Fresnel: E(P) = ∫ A(Q) · (1+cosθ)/2 · e^ikr/r dS | Single slit: sin θ_min = mλ/a

Huygens' Principle (1678)

Christiaan Huygens proposed that every point on a wavefront is itself a source of new secondary spherical wavelets that spread forward at the same wave speed v. The next wavefront is simply the common tangent — the envelope — of all these secondary wavelets.

This single idea explains why waves bend around corners (diffraction), why they change direction at boundaries (refraction via Snell's law), and why two coherent sources create bright and dark fringes (interference).

For a single slit of width a, destructive interference (dark fringes) occurs at angles where sin θ = mλ/a (m = ±1, ±2, …). For a double slit with separation d, bright fringes appear at d sin θ = mλ.