Eikonal & Wavefronts

Source & Medium

Parameters

Wave speed / wavelength: 30 px Index n₁: 1.0 Index n₂ (2nd region): 1.5 Animation speed: 1.0x

Eikonal Equation

|∇S|² = n(x,y)²

S = optical path length
Wavefronts: S = const
Rays: perpendicular to wavefronts

Huygens: each point on
wavefront = new source

Snell: n₁sinθ₁ = n₂sinθ₂
(continuity of S across interface)

Fermat's Principle

δ∫n(r)ds = 0

Light follows paths of
stationary optical path
length (not necessarily
minimum — also maximum
or saddle in some cases)

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