1. What Huygens’ principle says
Huygens’ principle gives a simple and intuitive way to understand how waves move forward. It states that:
Every point on a wavefront acts as a source of tiny secondary wavelets, and the new wavefront is the surface tangent to all these wavelets.
This principle works for all kinds of waves — water waves, sound waves, and especially for light in wave optics.
2. Why Huygens’ principle is useful
Instead of imagining light as straight rays, Huygens’ principle lets me visualise how a wavefront bends, spreads, or changes direction when it meets an obstacle or a medium boundary. This helps explain:
- reflection
- refraction
- diffraction
- shape of wavefronts
3. Wavefronts in Huygens’ picture
A wavefront is a surface on which all points vibrate in phase. Huygens’ principle uses these surfaces as the starting point to predict the next position of the wave.
3.1. Types of wavefronts
- Plane wavefront: arises from a distant source.
- Spherical wavefront: produced by a point source.
- Cylindrical wavefront: produced by a long narrow source like a slit.
4. Applying Huygens’ principle
To find the new position of a wavefront:
- Consider each point of the current wavefront as a source of circular (or spherical) secondary wavelets.
- Let these wavelets expand for a small time.
- The new wavefront is drawn as a surface touching the outermost points of these secondary waves.
This superposition of wavelets builds the next wavefront.
5. Explaining reflection using Huygens’ principle
When a wavefront strikes a reflecting surface, each point on the boundary behaves as a source of new wavelets. The reflected wavefront forms such that the angle of reflection equals the angle of incidence.
5.1. Reflection law from wavelets
The tangent drawn to the new wavelets makes the reflected wavefront. A simple geometric construction shows that:
\( \angle i = \angle r \)
matching the familiar law of reflection.
6. Explaining refraction using Huygens’ principle
When a wavefront moves from one medium to another, its speed changes. Because different parts of the wavefront reach the boundary earlier or later, the wavefront bends — this is refraction.
6.1. Deriving Snell’s law
Using the geometry of secondary wavelets in two media with speeds \(v_1\) and \(v_2\), Huygens’ principle gives:
\( \dfrac{\sin i}{\sin r} = \dfrac{v_1}{v_2} = \mu \)
This is exactly Snell’s law.
7. Explaining diffraction
When a wavefront meets a small opening or edge, only a portion of it continues. The remaining edge of the wavefront acts like a new source of wavelets, causing the wave to bend into the shadow region. This explains diffraction patterns clearly and naturally.
8. Limitations of Huygens’ principle
Huygens’ principle does not explain everything:
- It does not naturally include the idea of amplitude distribution.
- It cannot fully explain the exact intensity pattern of diffraction (Fresnel’s additions fixed this).
- It treats light as if secondary wavelets spread in all directions, but modern understanding ties this to electromagnetic fields.
Still, it remains one of the simplest conceptual tools to understand wave behaviour.
9. Why Huygens’ principle works well for light
Even though Huygens proposed the idea before electromagnetic theory existed, his construction turns out to match how wavefronts evolve in Maxwell’s equations. This makes it a powerful and intuitive model for studying wave optics.