Huygens–Fresnel principle
As such, the Huygens-Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.
He was able to provide a qualitative explanation of linear and spherical wave propagation, and to derive the laws of reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures and screens, commonly known as diffraction effects.
To obtain agreement with experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, and also an obliquity factor.
These assumptions have no obvious physical foundation, but led to predictions that agreed with many experimental observations, including the Poisson spot.
In 1882, Gustav Kirchhoff analyzed Fresnel's theory in a rigorous mathematical formulation, as an approximate form of an integral theorem.
[10] In 2021, Forrest L. Anderson showed that treating the wavelets as Dirac delta functions, summing and differentiating the summation is sufficient to cancel reverse propagating waves.
[11] The apparent change in direction of a light ray as it enters a sheet of glass at angle can be understood by the Huygens construction.
These wavelets propagate at a slower velocity in the glass, making less forward progress than their counterparts in air.
The arbitrary assumptions made by Fresnel to arrive at the Huygens–Fresnel equation emerge automatically from the mathematics in this derivation.
[13] A simple example of the operation of the principle can be seen when an open doorway connects two rooms and a sound is produced in a remote corner of one of them.
In order to get an agreement with experimental results, Fresnel found that the individual contributions from the secondary waves on the sphere had to be multiplied by a constant, −i/λ, and by an additional inclination factor, K(χ).
Kirchhoff showed that in many cases, the theorem can be approximated to a simpler form that is equivalent to the formation of Fresnel's formulation.
Above derivation of K(χ) assumed that the diffracting aperture is illuminated by a single spherical wave with a sufficiently large radius of curvature.
Huygens' theory served as a fundamental explanation of the wave nature of light interference and was further developed by Fresnel and Young but did not fully resolve all observations such as the low-intensity double-slit experiment first performed by G. I. Taylor in 1909.
[18] The wave function presents a much different explanation of the observed light and dark bands in a double slit experiment.
Homogeneity of space is fundamental to quantum field theory (QFT) where the wave function of any object propagates along all available unobstructed paths.
When integrated along all possible paths, with a phase factor proportional to the action, the interference of the wave-functions correctly predicts observable phenomena.
Every point on the wavefront acts as the source of secondary wavelets that spread out in the light cone with the same speed as the wave.
