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When refraction takes place at the interface of two media, wavefronts can be extended to intersect as below:

ref.

At point of intersection, light requires no time to travel between the wavefronts. However, between other point on the wavefront, time is rquired by the light to travel.

This clearly contradicts Huygens' principle which states that the time taken by light to travel between two wavefronts is irrespective of path taken by it.

What am I missing?

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  • $\begingroup$ The Huygens principle states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. Throw a ball in a poll. The generated wave reach to wall of pool at different time. This because of the points on wall meet wavefront at different times. When light passes from one medium to another, it refracts at the interface. $\endgroup$
    – Sancol.
    Commented Mar 1 at 7:34
  • $\begingroup$ According to Huygens’s principle, each point on the incident wavefront becomes a source of secondary wavelets. These secondary wavelets propagate in the new medium, and their envelope forms the refracted wavefront. So that, part of wave front still doesn't reach to intersection of two media and part of it refracted. $\endgroup$
    – Sancol.
    Commented Mar 1 at 7:58
  • $\begingroup$ @Sancol. Ah, I see, so it can be said that these point on the extension of the wavefronts do not lie on the locus of wavefront? $\endgroup$ Commented Mar 1 at 9:34

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The wavefronts don't intersect anywhere. The wavefronts are perpendicular to the rays everywhere (pretty much by definition). Rays and wavefronts look like this:

enter image description here
(image from question "What does the wave look like during refraction?")

In medium 2 the waves travel with slower speed than in medium 1. Hence in medium 2 the wavefronts are denser spaced than medium 1. It follows from Huygens' principle that the wavefronts (and hence also the rays) bend at the border between the media.

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It is true that in the optical (high frequency) limit the rays are orthogonal to the constant phase surfaces, the wavefronts, and the optical path length along these rays between any two wavefronts is the same. In other words, the optical distance between two between wavefronts is independent of the ray. This property of wavefronts is sometimes viewed as the manifestation of Huygens's principle in the geometrical optical limit. It can be shown to be essentially equivalent to the various forms the laws of optics are derived including Snell's law of refraction, Fermat's principle, Malus-Dupin law, Lagrange's invariant, etc.

But this property of waveforms does not apply to your question because the extension in the dielectric of the wavefront that is propagating in vacuum is not a wavefront, it is a geometric surface but it is not the one that propagates. Rays may start from a single point and, such as a focus, for example, and then the geometrical optic wavefront may degenerate into a singularity; this is where geometrical optics actually fail to describe real physics and you need physical, ie., wave optics. But in your question you do not have that, in fact the incident wavefront breaks into two planes continuously but not smoothly joined at the interface, kind of bending and propagates while maintaining the optical distance between them.

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