Spherical Huygens Waves and Diffraction: Why Does the Situation Look Different?

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kooba
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Short question, but I can't figure it out - when we have a diffraction on any obstacle, which is construction of spherical Huygens waves, why the situation presents as it is shown on the first picture and not like on the second picture, what could actually be expected, as we consider spherical Huygens wavelets (third picture).
Of course in such situations, there wouldn't be any shades, but how it is, from the Huygens construction, that the situation is as it is on the first picture.
 
Attachments
  • Diagram of a plane wave with three vertical blue wavefronts passing a black vertical barrier, with small arcs curving around the barrier's upper edge, illustrating diffraction.
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  • Diagram of plane wavefronts, drawn as three vertical blue lines, passing a vertical black barrier with a small gap; curved blue arcs spread out beyond the gap, showing diffraction.
    2.gif
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  • Diagram of plane wave fronts (blue vertical lines) meeting a black vertical barrier with an opening, showing circular wavelets spreading out from the gap on the right side of the barrier.
    3.gif
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Discussion

Not a complete answer... but you must sum the spherical waves as in the 3rd picture over the entire available wave-front (from the edge of the barrier on up) and not just get a contribution from that one point. Given Huygen's principle applies even if you have no barrier and given you have no lateral contribution from one wave-front of a planar wave (so it remains a planar wave as it propagates) then there should be some canceling.

I think the first picture is close but not perfectly accurate. I think you should get a qualitative picture like the 2nd but with sharply (gaussian like e^(-theta^2) ) diminishing of amplitude. So more like a hybrid of pictures 1 & 2. [Working from distant memory here though. I haven't looked at this in a while.]

But in all, to answer "why" do the integration and see what the math tells you.