Huygens' Principle

Huygens's principle is a rather simple idea that we have already seen quite a bit of in this module. It assumes that at any given moment, each point on a wave front can be considered as the source of a spherical wave expanding from that point. These new spherical waves combine to form the new wave going forward.

This turns out to be a nice way to once again show how refraction works. In the gif below, the wave is incident from vacuum onto the surface of a medium of index n=1.45. An array of dipole emitters lines the interface between vacuum and glass. The 'spherical' waves emitted by the dipoles now travel different speeds in vacuum (left side) than they do in glass (right side).

As a result, the waves emitted into the glass are delayed compared to those in vacuum (because they travel at a speed v=c/n) and form a continuous wave front at a steeper angle than they would in free space. The new wave front angle and wave propagation direction are given precisely by the Law of Refraction.

It is worth noting that Huygens' principle is more of a colloquial description of how light could propagate rather than an exact, mathematical formalism. We will review a much more mathematically sounds theory later in the semester but Huygens' principle provides a nice picture for how waves propagate.