Huygens Principle & Diffraction

Every wavefront point is a secondary wavelet source — their interference builds the diffraction pattern

14λ
18
20

Huygens-Fresnel Principle

Each point on a wavefront acts as a source of spherical secondary wavelets. The field at any point P is:
U(P) = ∫_aperture A(Q) e^{ikr}/r dS

Fraunhofer (far-field, L ≫ a²/λ): intensity pattern
Single slit: I(θ) = I₀ sinc²(πa sinθ/λ)
Double slit: I(θ) = I₀ sinc²(β) cos²(δ)
where β=πa sinθ/λ, δ=πd sinθ/λ

Fresnel (near-field): includes quadratic phase terms, requires Fresnel integrals C(u)+iS(u).

Interference & Coherence

The first single-slit minimum occurs at sin θ = λ/a — wider slits diffract less. The first double-slit minimum (single slit envelope) at sin θ = λ/a, with interference fringes spacing sin θ = λ/d.

The number of visible fringes under the central maximum ≈ d/a. Missing orders occur when a diffraction maximum coincides with an interference minimum.

Huygens' principle explains: reflection (Snell's law), refraction (wavefront bending at boundaries), and diffraction — all as consequences of wavelet superposition.