§ 9. Light Wavefront & Huygens–Fresnel Principle (Grade 9–11)
Huygens' secondary spherical wavelets and plane wavefront refraction. Every point of a medium reached by a light wavefront becomes a source of secondary hemispherical wavelets, whose envelope forms the new wavefront at the next instant.
Theory Summary & Scientific Mechanism
According to the Huygens–Fresnel principle, every point on an advancing light wavefront acts as a point source of secondary spherical wavelets. The wavefront surface at a later instant t + Δ t is formed by the forward tangent envelope of all these secondary wavelets.
When an oblique plane wavefront strikes the interface between media of refractive indices n₁ and n₂ > n₁ at angle α, its phase velocity drops from v₁ = c/n₁ to v₂ = c/n₂. While the outer edge of the wavefront travels distance BC = v₁ Δ t = ABsin α in medium 1, the edge that entered medium 2 expands only to radius AD = v₂ Δ t = ABsin γ. Taking the ratio immediately proves Snell’s Law of Refraction: (sin α)/(sin γ) = (v₁)/(v₂) = (n₂)/(n₁).
Observe in 3D how entering optically denser glass (n₂ > n₁) compresses the spacing between wavefront crests (λ₂ = λ₀ / n₂) while keeping frequency ν constant, rotating the wavefront normal toward the interface normal (γ < α).
Everyday Analogy
Drop a pebble in a pond near a narrow gap: the ripple squeezes through and spreads out in circles again! And just as a marching band turns when stepping from pavement onto sand at an angle, light bends when entering glass!
Interactive Question & Derivation
A plane light wavefront passes from air (n₁ = 1.0) into optically denser glass (n₂ = 1.5) at an angle of incidence α > 0. Why does the plane of the light wavefront bend toward the normal (γ < α)?
- A: Because the light frequency ν increases by 1.5× inside the glass
- B: Because Huygens' secondary spherical wavelets propagate slower in glass (v₂ = c/n₂ < c) and the wavelength spacing λ₂ = λ₀/n₂ compresses
- C: Because the light wavefront accelerates inside the glass (v₂ > c)
Study Hint: When a light wave enters a denser medium (n₂ > n₁), its phase speed v = c/n drops. Does the refracted ray bend toward or away from the normal?
Proof & Explanation: According to Huygens' principle, as an oblique light wavefront reaches the interface, its left edge enters the glass first and emits secondary hemispherical wavelets that travel at a lower phase velocity v₂ = c/n₂. While the right edge travels v₁ Δ t in air, the left edge travels only v₂ Δ t in glass, rotating the wavefront envelope so that sin α / sin γ = v₁ / v₂ = n₂ / n₁.
Key Equations & 3D Simulation Parameters
n₁sin α = n₂sin γ, v₂ = (c)/(n₂), λ₂ = (λ₀)/(n₂)
- Wavefront incidence angle α: 10 … 75 ° (default: 45 °)
- Medium refractive index n₂: 1.15 … 2.4 (default: 1.55)
- Vacuum wavelength λ₀: 400 … 700 nm (default: 540 nm)
- Huygens wavelet sources N: 3 … 7 sources (default: 5 sources)