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Reflection of a plane wave: proving the law of reflection sheet
3-mark answer frame

Using Huygens' principle, prove the law of reflection. Draw a labelled diagram.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · State the principle used. Each point on a wavefront sends out secondary wavelets; their forward envelope is the new wavefront.
  2. 2 · Draw the construction. [Surface MN; incident wavefront AB at angle i; BC = vτ; arc of radius vτ centred at A; tangent CE as reflected wavefront; rays, normals, i and r marked]
  3. 3 · Write the distances. In time τ, B reaches C, so BC = vτ. The wavelet from A has radius AE = vτ (same medium).
  4. 4 · Prove the triangles congruent. In triangles ABC and AEC: AC common, BC = AE, ∠B = ∠E = 90°. So they are congruent (RHS).
  5. 5 · Conclude. ∠BAC = ∠ECA, so i = r.
  6. 6 · Real life. A DTH dish uses reflection to bring satellite signals to its focus.

Scoring tip: Mark i and r between the wavefronts and the surface, and also between the rays and the normals.