Refraction huygens principle?

Question

Explain, using Huygen’s principle, how refraction occurs due to a change of wave speed as the wave moves from one medium to another.

Answer 1

From ref. 1, Huygens' principle: The principle that any point on a wave front of light may be regarded as the source of secondary waves and that the surface that is tangent to the secondary waves can be used to determine the future position of the wave front.
Basically this means that each point of contact of a wavefront along the boundary between media of different refractive indices N(m) becomes a point-source emitter of waves whose velocity depends on N(m). The tangents of the circles representing the point-source emissions define the refraction angles.
This is well illustrated in ref. 2 (second step).

Answer 2

Huygens Principle Definition

Answer 3

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Wave diffraction in the manner of Huygens.The Huygens–Fresnel principle (named for Dutch physicist Christiaan Huygens, and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation (both in the far field limit and in near field diffraction). It recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. This view of wave propagation helps better understand a variety of wave phenomena, such as diffraction.

For example, if two rooms are connected by an open doorway and a sound is produced in a remote corner of one of them, a person in the other room will hear the sound as if it originated at the doorway. As far as the second room is concerned, the vibrating air in the doorway is the source of the sound. The same is true of light passing the edge of an obstacle, but this is not as easily observed because of the short wavelength of visible light.

Huygens principle mathematically follows from the fundamental postulate of quantum electrodynamics – that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point. Not only light quanta (photons), but electrons, neutrons, protons, atoms, molecules, and all other objects obey this simple principle.