Huygens' Principle
Every point on a wavefront is a new source, and the laws of reflection and refraction follow.
Lesson at a glanceShow the key points
- Points on any surface reached by a wave act as secondary sources sending out wavelets; the disturbance beyond is their superposition.
- Huygens construction: the new wavefront is the forward envelope (common tangent) of the wavelets.
- Reflection: wavelets from a mirror build a reflected wavefront; congruent triangles give angle of incidence = angle of reflection.
- Refraction: wavelets in medium 2 travel at v₂, giving sin i / sin r = v₁/v₂ = μ₂₁ (Snell's law); rays and normal are coplanar.
- Light bends toward the normal entering water, so wave theory needs v_water < v_air, opposite to Newton's corpuscles. Experiment sided with waves.
Huygens had a simple way to predict where a wave goes next: treat every point the wave reaches as a tiny new source. From that one idea the laws of reflection and refraction drop out.
Secondary wavelets
Draw any surface around a light source. Light reaching points beyond it must cross that surface. Huygens argued that each point of the surface, once the wave arrives, starts vibrating and acts as a new source of spherical waves. He called these points secondary sources and their waves secondary wavelets.
The new wavefront is the envelope
Take a spherical wavefront around a point source and let every point on it send out a short wavelet. After a time t each wavelet is a sphere of radius vt. Just inside the outer surface touching all of them (their envelope), the wavelets meet in step and reinforce. Deeper inside, wavelets from neighbouring points arrive with opposite signs and cancel. So the disturbance ends up on the envelope:
In a uniform medium we only take the envelope in the forward direction. If the wave meets a new medium, wavelets going backwards (the reflected wave) must be included too.
Reflection from Huygens’ principle
A plane wavefront AB meets a mirror obliquely. Its edge touches the mirror at A at t = 0; the other edge reaches C at time t, after travelling BC = vt. Meanwhile the wavelet from A has grown to a hemisphere of radius vt. Every point between A and C is reached a little later and sends a smaller wavelet. All of them touch one line through C, tangent to A’s wavelet at D. That line CD is the reflected wavefront.
The right-angled triangles ABC and ADC share the side AC and have AD = BC = vt, so they are congruent, and ∠BAC = ∠DCA. These are the angles of incidence and reflection. So i = r, and the rays and the normal all lie in the plane of the drawing.
Refraction from Huygens’ principle
Now the wave crosses into medium 2, where light is slower (speed v₂ instead of v₁). While the far edge of the wavefront covers BC = v₁t in medium 1, the wavelet from A grows only to radius AD = v₂t. The tangent CD from C is the refracted wavefront. In the two right-angled triangles:
Light in air meets glass (μ = 1.5) at 50° to the normal. Find the angle of refraction.
- 1Every point reached by a wave acts as a source of secondary wavelets.
- 2The new wavefront is the forward envelope of the wavelets.
- 3Applied at a mirror, it gives i = r; at a boundary, sin i / sin r = v₁/v₂ = μ₂₁ (Snell's law).
- 4Bending toward the normal means light is slower in the denser medium, as later measured.
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