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My book mentions the following cases while discussing Huygens' Principle and wavefronts:

i) Light emerging from an incandescent straight wire: wavefronts are cylindrical and coaxial with the straight source as their common axis.

ii) Light emerging from a narrow straight single slit: wavefronts will be semi-cylindrical.

Here, I apply a qualitative analogy:

If the rays (wave normals) are compared to the increasing direction of electric field for a given charge distribution, then the wavefronts may be compared to the corresponding equipotential surface. For instance, point charge corresponds to light emerging from a point source, both of which result in spherical equipotential surfaces (wavefronts).

Similarly, case (i) is consistent with a (infinite) line charge distribution, which has cylindrical, coaxial equipotential surfaces

Continuing the said analogy, I would like to know what will be the equivalent "electric field" and "equipotential surface" for case (ii)

A colleague of mine argues that when considering slits, unlike the straight line, one is also inherently talking about a direction. But I believe, per Huygens principle the slit is an idealized source without considering the "history" of how the light got there in the first place.

Sought is a mostly qualitative argument which is consistent with the said analogy, or one which points out possible flaws in the latter.

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  • $\begingroup$ You might find these 3blue1brown videos useful - Optical Puzzles $\endgroup$
    – mmesser314
    Commented Nov 8 at 3:56
  • $\begingroup$ Practically, the output from one point on the incandescent wire won't be coherent from the output on another point on the wire, and that means there won't be cylindrical wavefronts. If you're going to ignore this fact, then you may as well also ignore the fact that the emission from an incandescent source isn't linearly polarized. $\endgroup$
    – The Photon
    Commented Nov 8 at 3:58

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But I believe, per Huygens principle the slit is an idealized source without considering the "history" of how the light got there in the first place.

What this means is, if you illuminate the slit with a coherent source, you can achieve the (semi) cylindrical wavefronts you have supposed emanate from the incandescent wire.

If the short dimension of the slit is on the order of one wavelength or smaller, you will also find that the slit preferentially passes one linear polarization of light --- with the E filed perpendicular to the slit.

This means the slit scenario is very closely consistent with the behavior you supposed the incandescent wire would produce.

The wire itself, on the other hand would not produce cylindrical wavefronts because the emission from different points on the wire would not be mutually coherent.

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  • $\begingroup$ +1 for picking the specific statement that I would also have picked up to contend about. It is by comparing the experimental results with the mental model of the simplistic Huygen's principle assumption of "history-less coherent uniform wavefront" that we realise that temporal and spatial coherence of a wave is quite important. There are entire fields of study into such issues, with amazing applications! The companies making wavefront sensors have carved out an amazing niche for themselves. Very amazingly good work, but also meaning that they charge an arm and a leg. $\endgroup$
    – naturallyInconsistent
    Commented Nov 8 at 4:44
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In general charges create electric fields (non magnetic) and they are not described or associated with wave characteristics (not wavefronts), these fields create forces on other charges .... yes it is radial (also travels at c). A charge can effect many other charges.

Light involves propagation of energy (not forces) ... QM would say light has a probability of propagate in any racial direction .., but eventually chooses one ray direction and propagates per Maxwell's equation as a localized wave in the EM field with both E and M components. It travels at c but only evenetually effects one other electron/atom.

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