Huygens' Principle: Wave Propagation & Phenomena

Huygens' Principle: Understanding Wave Propagation

Huygens' Principle is a wave propagation model that helps explain various wave phenomena. It states that a wave propagates as a wave front or surface connecting all points reached by the wave motion at the same instant. Every point of an isotropic medium which experiences a disturbance behaves as a source emitting secondary waves (or wavelets) that propagate in the direction of the disturbance. The surface tangent to all these wavelets at a given instant forms the next wave front. The radius of the wavelets at any instant is vt (velocity × time).

Wave Reflection

When a wave propagating through one medium reaches the boundary with a different medium, part of the wave is reflected and continues to spread through the original medium. The other part is transmitted into the new medium, where, being different, it will propagate with a different speed and hence a different wavelength (v = λf, where v is speed, λ is wavelength, and f is frequency) because the frequency remains constant. This change in speed can also change its direction.

Consider an incident wave advancing with flat wave fronts. When it contacts the surface separating the two media, each point of contact becomes a source emitting reflected spherical wavelets. If the speed of propagation in that medium is v, the secondary wave emitted by point A will have a radius equal to v after one second. However, the incident wave front will have moved to A', which then becomes a new source of wavelets. The next second, the secondary wave emitted by A' will have a radius v, while that emitted by A will have a radius of 2v. A fundamental principle of reflection is that the angle of incidence equals the angle of reflection.

Wave Refraction

The same points on the incident wave front that act as sources for reflected waves can also act as sources for refracted waves, which spread into the new medium. If the speed of propagation in the new medium is v', a secondary refracted wave emitted from point A will have a radius of 2v' two seconds after the incident front reaches A. Meanwhile, the wave emitted by A' (the point reached one second later) will have a radius of v' at that same instant.

Key principles of refraction:

• If v (speed in original medium) is greater than v' (speed in new medium), the direction of the refracted wave fronts propagates away from the normal to the boundary. In this case, the angle of refraction is greater than the angle of incidence.
• If v' is greater than v, the direction of the refracted wave fronts propagates towards the normal. In this case, the angle of refraction is less than the angle of incidence.

Wave Diffraction

Diffraction is the phenomenon whereby a wave changes its propagation direction when encountering openings or obstacles. The points on the portion of the wave front passing through an aperture become new minor emission sources (wavelets). The shape of the diffracted wave fronts depends on the dimensions of the aperture relative to the incident wavelength.

Diffraction effects:

• If the opening is large compared to the wavelength, diffraction is hardly noticeable.
• If the opening is similar in size to the wavelength, diffraction becomes significant and pronounced.