Using Huygens' principle, deduce Snell's law of refraction for a plane wavefront. Show that the frequency of light does not change but its wavelength does. Draw a labelled diagram.

1. 1 · State Huygens' principle in one line. Every point on a wavefront sends out secondary wavelets; their forward envelope is the new wavefront.
2. 2 · Draw the construction. [Surface PP′; medium 1 (v₁) above and medium 2 (v₂) below; incident wavefront AB at angle i; BC = v₁τ; arc of radius v₂τ from A; tangent CE as refracted wavefront at angle r; rays and normals]
3. 3 · Write the distances covered in time τ. BC = v₁τ in medium 1; AE = v₂τ in medium 2.
4. 4 · Use the two right triangles.
   • sin i = BC/AC = v₁τ/AC
   • sin r = AE/AC = v₂τ/AC
   • sin i / sin r = v₁/v₂
5. 5 · Bring in the refractive index. v₁ = c/n₁ and v₂ = c/n₂, so n₁ sin i = n₂ sin r: Snell's law.
6. 6 · Frequency and wavelength. Frequency is fixed by the source. BC and AE take the same time, so λ₁/λ₂ = v₁/v₂: the wavelength is shorter in the denser medium.
7. 7 · Real life. A coin in a bucket of water looks raised for this reason.
8. 8 · Close in one line. So, sin i / sin r is constant for a pair of media, which is Snell's law.

Scoring tip: Make the arc from A visibly shorter than BC when medium 2 is denser; examiners check this.