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I understand that diffraction is the bending of light around sharp edges. Using Huygens' theory, one explains this by imagining a plane wave hitting a slit. Normally, each point on the plane wave would act as a spherical wavefront, and the common envelope of all these wavefronts would also be a plane wave. When part of this wave is blocked by an obstacle,the 'top-most or bottom-most' part of the new wave would propagate spherically as there is no longer anything above or below, to flatten the wavefront. Hence, our wavefront now looks more like this:

enter image description here

I know this can also be explained using the uncertainty principle, but my goal is to understand Huygens' theory properly.

Anyway, as we can see, the wavefront spreads into the geometric shadow. Now, all this is well and good, but I don't seem to understand where do the 'fringes' come from. Huygen's theory seems to explain why light bends around obstacles, but not why we should get a fringe pattern in case of a single slit.

Many books suggest, this is because the secondary sources on this new 'semi-circularish' wave-front, produce spherical waves that interfere with one another, to create points of constructive and destructive interference. This self interaction doesn't seem to make sense to me.

In case of the simple double slit experiment, the idea of two separate wavefronts interfering with each other to create bright and dark bands seem to make sense.

But now, imagine a single source from which the wavefront spreads in all directions i.e. a source with a spherical wavefront. Now suppose, there is a screen in front of the source. There would be an uniform intensity distribution on the screen. However, if I now put a single slit between the source and the screen, the intensity pattern would show fringes. The case with the slit is explained by saying that after the wave comes out of the slit, each point acts as a secondary source, and the waveforms from these sources interfere constructively and destructively. However, if there was no slit, even then each point on the spherical wavefront would act as secondary source. However, we don't consider the interference of the waves from these secondary sources in the absence of a slit. Else, we would get a bright and dark band pattern by simply shining light on an object.

In any scenario, each point on a wavefront, acts as a secondary source. However, after passing through an obstacle, these secondary sources interfere with each other to create bright and dark patterns. But using this logic, if we just consider the simple spreading out of light from a point source, then each point on this spherical wavefront should also act as secondary sources which should interfere with each other. However, this would cause a diffraction patter on any screen irrespective of the presence of an obstacle.

Can anyone help me understand this.

( I know how the fringes appear using integration over a wave and then finding conditions of maxima and minima. I just want to understand this, by using huygens principle ). If light interferes with itself, then shouldn't we see dark and bright bands everywhere ? Why do we need a slit?

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    $\begingroup$ I'm not sure I understand the question. I don't know which of these is helpful: 1) The light and dark features in your photograph are not fringes. They represent the (squared) amplitude of the disturbance. The locus of points of constant intensity are phase fronts, the locus of constant phase. 2) The Huygens wavelets generated at every point on a spherical wave do interfere. The result of the superposition is uniform (fringeless) pattern on a screen. $\endgroup$
    – garyp
    Jan 9 at 13:56
  • $\begingroup$ @garyp I used the photograph as reference to show the bending around the edges. I'm talking about the fringes that would have formed on a screen, had I kept one in front of it. $\endgroup$
    – RayPalmer
    Jan 9 at 13:59
  • $\begingroup$ @garyp huygen's principle explains well, why the wavefront bends around the edges. However, the different secondary wavelets interfering with each other to form bright and dark bands keeps confusing me. Like in a plain wave in vaccuum, the secondary wavelets would interfere too, but if you shine light on a screen you don't see fringes. $\endgroup$
    – RayPalmer
    Jan 9 at 14:01
  • $\begingroup$ Do you expect a plane wave to produce a fringe pattern? $\endgroup$
    – garyp
    Jan 9 at 14:02
  • $\begingroup$ @garyp ofcourse not, that is exactly why the confusion arises. In many books, the fringe pattern in single slit diffraction is explained by saying that the secondary wavelets on the semicircular wavefront interfere constructively/destructively to give a fringe pattern. However, if we have a source radiating spherical waves in all directions, even there, the secondary wavelets interfere, but instead, we get a constant intensity distribution. $\endgroup$
    – RayPalmer
    Jan 9 at 14:07

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Huygens' principle does not explain interference. It applies to incoherent waves. You need wave theory to describe interference which results from wave coherence.

"Else, we would get a bright and dark band pattern by simply shining light on an object." These bands exist but they move with the speed of light or alternate with the frequency of the light. They do not form a stationary interference pattern.

We need a perturbation such as a slit to get a stationary pattern.

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  • $\begingroup$ Can you elaborate on this a little more. I've done the electric field integral for single and double slit and found the interference fringe pattern for both cases. However, I don't understand this 'stationary interference pattern' idea. I thought, all interference patterns must be stationary. Can you elaborate on how plane waves create a oscillating interference pattern, and how does a perturbation such as a slit, make this stationary ? $\endgroup$
    – RayPalmer
    Jan 12 at 15:48
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When I was looking at this recently, I found it quite instructive to do a numerical simulation of the illuminated slit as a large number of 2D 'point sources' arranged in a line. Your model doen't actually need to include very many of these sources before you can start seeing the 'fringes' in the form of areas of constructive and destructive interference, fanning out radially from the edges of the slit.

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  • $\begingroup$ A better approach is to do the Feynman path integral simulation, examples on this site. $\endgroup$ Jan 12 at 0:51
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Interference for light is a misleading idea, but it is taught because it does offer value at the beginner level. In the double slit or single slit for light the bright areas have all the energy (photons) the dark areas none (no photons). In higher (masters) physics the Feynman path integral is the accepted explanation for the "interference". The integral looks at all paths and sums the amplitude, for example a computer sim would calculate the path length for many paths from source thru various paths in the slits to the all the possible screen points. By keeping track of phase the amplitudes are summed, it results in paths that are integer multiples of the wavelength (i.e. ones that are resonant)become the preferred paths, and in some paths the amplitude sums to zero!

There are some good examples on this site, search "Feynman path integral".

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  • $\begingroup$ Isn't that exactly what interference is? $\endgroup$
    – my2cts
    Jan 11 at 10:47
  • $\begingroup$ @my2cts The path integral superimposes/interferes many paths and mathematically finds the preferred/highest probability ones. It could mean that many virtual photons are emitted and interfered ( i.e. no energy transfer only forces). But 2 real photons never interfere .... and unfortunately this is what is in most peoples understanding. $\endgroup$ Jan 12 at 0:54
  • $\begingroup$ @PhysicsDave ah so, in case of plane wave, as in just shining light on an object, all the paths are equally probable, since there is no obstacle or anything, and so we get a constant intensity at some distance, and this intensity decreases over distance. In case of a slit, all paths are no-longer equally probable, and so, we get interference fringes, is that about right ? $\endgroup$
    – RayPalmer
    Jan 12 at 15:50
  • $\begingroup$ @RayPalmer You say you did the electric field integral? Tell me more... Yes you are getting the drift but .... 1) The slits experiments are quite tight geometrically .. the slits are very narrow and the source small, many photons will actually reject the slit (like a mirror). 2) doing the Feynman path integral is really adding many phases of a virtual field, no energy is transmitted only the forces of the excited electron in the EM field, eventually a photon is emitted, highly tending to travel paths whole integer amounts of their wavelength, I like to say the paths are resonant! $\endgroup$ Jan 12 at 23:57
  • $\begingroup$ @RayPalmer So the real explanation is complicated ... virtual forces .... virtual photons ..... Feynman path integral. No high school teacher in their right mind would teach it! Tends to be a lot easier just to say "interference". $\endgroup$ Jan 13 at 0:03
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In any scenario, each point on a wavefront, acts as a secondary source.

I think that's what confuses you. Once the wavefront is formed, there is no reason why it should interact with itself because everything is traveling at the same "speed", phase (that's what a wavefront is). Once you insert an obstacle you are deforming this wavefront, and generating new ones - they will interfere and generate the interference pattern.

Also, a plane wave generates an interference pattern as well...(simply imagine the plane wavefront being formed by the "edge" part of an infinite number of spherical waves).

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  • $\begingroup$ A water wave going thru a single slit does NOT generate an interference pattern. While water and light do share some wave similarities they also behave very differently in other areas. $\endgroup$ Jan 12 at 0:56
  • $\begingroup$ I do not see your point, I was not talking about water and I do not see any reference to it in the question - that I assume concern light propagation. $\endgroup$
    – gbon
    Jan 12 at 8:03
  • $\begingroup$ The Huygens principle has historically been used to explain light interference for its simplicity and practicality in teaching, but a photon can not split and generate new copies of itself, that splitting analogy is better for matter waves. The Feynman path integral explains light patterns thru slit(s). $\endgroup$ Jan 12 at 15:21
  • $\begingroup$ I still fail to see your point regarding the answer/comment. Please, when replying refer to what I answered or comment. I never talked about "splitting" photons, I talked about wavefront. $\endgroup$
    – gbon
    Jan 13 at 8:10
  • $\begingroup$ A plane wave of light is not required to cause interference, the term wavefront of light does NOT imply everything is traveling in phase, most often it is not. You invoke the Huygens principle when you say "generating new ones" but you fail to see that a water wave going thru a single slit produces NO interference ... and thus Huygens principle is not applicable to light. $\endgroup$ Jan 14 at 17:46

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