Figure: Huygens principle illustrated and explicated

Caption: The diffraction pattern formed by a broken wavefront can be understood and calculated to some degree using Huygens principle (correctly Huygens' principle, but no one says that).

In the image, one sees diffraction at an aperture. The yellow dots are a representative sample of the continuum of pseudo point sources of electromagnetic radiation (EMR) making up a broken wavefront of plane waves. The continuum of pseudo point sources gives rise to the transmitted and diffracted wave according to the scientific model of Huygens principle---which is only an incomplete model of what diffraction happens NOT a fundamental description.

However, although the original Huygens principle is very approximate, the more advanced Huygens principle (formally called the Huygens-Fresnel principle) can be used to calculate very accurate diffraction patterns without using the full formalism of a href="http://en.wikipedia.org/wiki/Classical_electromagnetism">classical electromagnetism and this is often done (e.g., HZ-331).

Further explication:

1. Diffraction can be set up with a large number of discrete sources (e.g., in diffraction grating).

   However, diffraction happens ubiquitously whenever a wavefront is broken by obstacles with apertures being a special class of obstacle.

   The breaking of the wavefront can be understood to some degree as the creation of a continuum of pseudo point sources of electromagnetic radiation (EMR) all of which have a definite phase relationship to each other, and so lead to interference (i.e., diffraction). A definite phase relationship in wave phenomena is called coherence.

   The just-described model of diffraction on the breaking of a wavefront is called as a aforesaid Huygens principle.

2. Christiaan Huygens (1629--1695) in 1678 proposed Huygens principle to explain the reflection and refraction of light. Augustin-Jean Fresnel (1788-1827) extended Huygens principle to account for diffraction.

   Both scientists had to introduce extra and somewhat ill-defined hypotheses to make the minimalist Huygens principle yield valid predictions.

   Note one should actually say the Huygens principle or Huygens' principle, but customary usage is to just say "Huygens principle".

3. Huygens principle states that an obstacle/aperture causes all the points adjacent in some sense to where a wavefront is broken by said obstacle/aperture to act as point sources for spherical waves in some range of solid angle in roughly the forward direction. The point sources have coherence and this gives rise interference. The spherical waves from the pseudo point sources add to create a diffraction pattern via interference.

   Note the statement above is a vague qualitative rule that takes the aforesaid extra and somewhat ill-defined hypotheses to make the minimalist Huygens principle yield valid predictions.

4. Is Huygens principle a very general emergent principle of physical reality?
   1. There is an argument that it is (see Wikipedia: Huygens-Fresnel principle: Huygens' principle and quantum field theory).

   2. On the other hand, some argue that Huygens principle is only an emergent principle in a very limited sense and should be classified as a derived result.

      This is because Kirchoff's diffraction formula provides a quantitative model of light propagation from which Huygens principle can be derived along with extra conditions (replacing the aforesaid extra and somewhat ill-defined hypotheses) needed to make it quantitative (see Wikipedia: Kirchhoff's diffraction formula: Equivalence to Huygens-Fresnel equation).

      Kirchoff's diffraction formula itself can be derived from classical electromagnetism which is actually needed for a general exact treatment of the propagation of electromagnetic radiation (EMR) in the classical limit.

      For the argument that Huygens principle is just a derived result, see Wikipedia: Huygens-Fresnel principle: History.

   3. The difference between the two perspectives on Huygens principle seems to yours truly to be a matter of how carefully one defines Huygens principle.

      At the present moment, yours truly thinks the first perspective is best since Huygens principle holds for all physical waves (i.e., mechanical waves, electromagnetic wave, and quantum mechanical waves) and is exact in some limits.

      Of course, one needs the aforesaid extra hypotheses (which somehow are well defined) to make it exact in those limits.

5. As a bit of science history, Francesco Maria Grimaldi (1618--1663) was the first person to scientifically study the diffraction of light (see Wikipedia: Diffraction: History) and the first ones to propose the wave theory of light based on diffraction were Robert Hooke (1635--1703) qualitatively and Christiann Huygens quantitatively (see Wikipedia: Light: Wave theory and Wikipedia: Christiaan Huygens: Optics).

   It's a remarkable fact that the diffraction of light is almost unnoticeable in everyday life and it wasn't until the 17th century that anyone noticed it in the historical record???. Except for for very tiny apertures or obstacles, all people could see easily was the bright central fringe which is explained by geometrical optics. The tiny side fringes were also easily washed out light from sources other than those being affected by apertures or obstacles. Also, interference is wavelength dependent, and so polychromatic light tends to wash out the fringes.

   Interference/diffraction in water waves had been noticed since forever, but apparently without anyone studying it scientifically or even philosophically. It probably seemed too complex to understand before the idea developed in the Scientific Revolution of the 17th century of controlled experiment in which variables are cleanly identified and varied one at a time.

   In constrast to the wave theory of light, Pierre Gassendi (1592--1655) and Isaac Newton (1643--1727) proposed a corpuscular theory of light which was the dominant theory until circa 1800 (see Wikipedia: Light: Wave theory).

   The process of scientific acceptance of the wave theory of light was greatly advanced by the work of Thomas Young (1773--1829) in the early 19th century (Wikipedia: Thomas Young: Wave theory of light).

   In fact, both the wave theory of light and the corpuscular theory of light had much to offer.

   Note, yours truly would judge the wave theory of light to be a true emergent theory from classical electromagnetism, but NOT the corpuscular theory of light. And geometric optics is a true emergent theory from the wave theory of light. However, the "emergences" are ordered logically and not the order of discovery of the theories in history.

   Note also, the photon theory of light did NOT historically arise from the corpuscular theory of light although there are, of course, similarities.