# About the existence of secondary wavelets

Huygens principle said that "all point in a wavefront may be considered as a new source of wavelets, the tangent of these wavelets will form new wavefront,but,if we do experiments like creating water waves we won't see spherical wavelets emitting from the wavefront which makes me questioned if they are real or not or if they are just imaginary So the question is, do those secondary wavelets exist(you can see them) or just a tool to help you to find new wavefronts?

I'd like to suggest an analogy that might help to clarify the situation.

Consider a wave on a string. While this is obviously different from a light wave the propagation of the wave on a string is described by the same equation, the wave equation, as a light wave so mathematically it is similar.

Now consider some infinitesimal element on the string. That element doesn't know anything about the overall shape of the string. All it knows is that it is connected to a piece of string on its left and another piece of string on its right. Due to the tension in the string our element exerts a force on the string to its left and on the string to its right, and this situation is symmetrical in the sense that the left and right directions are equivalent.

So our element "radiates" symmetrically in both directions in the sense that it acts equally on the neighbouring elements to its left and right, and Huygens' principle emerges naturally. We really can describe an oscillating string as an infinite collection of point oscillators radiating symmetrically.

I chose a string because we've all twanged elastic bands or guitar strings so we have a good intuition for how they behave, but the same maths applies to a light wave. A light wave is just an electric field filling some region of space, and the wave is an oscillation travelling through this field just as a wave travels along a string. Like the string we can imagine some infinitesimal volume of space and the field in this volume acting equally in all directions on the field surrounding it. Again Huygens' principle emerges naturally.

Ultimately whether the secondary wavelets actually exist or not comes down to a matter of opinion. You can certainly decompose the wave into a sum of the secondary wavelets, and I hope I've convinced you that there is a good physical reason to treat each point in the electric field (or string) as radiating isotropically. My own view would be that yes Huygens' principle really does describe physically how a wave evolves.

When on an opaque screen you make a hole of the size of the wavelength or smaller and you let the wave hit the screen from practically any direction then on the other side of the hole a spherical wave will appear irrespective of the incident direction or the shape of the wave. The amplitude of the spherical wavelet emitted from the hole is proportional to the incident amplitude. If you do this along any of the incident wave's constant phase surfaces you can actually map the amplitude there by measuring the amplitude of secondary wavelet emanating from the hole. If you measure the relative phases of two such spherical wavelets then that will be the same as the relative phase between the two respective points of the incident wave. All these are evidence of the Huygens principle.

• You mean the secondary wavefront is caused by diffraction right? Commented Mar 11, 2022 at 2:58
• the secondary (spherical) wavelets and their secondary wavefront are not caused by diffraction, instead they are constituents of the propagating wave. Just as a sieve does not make a seed rather it separates the small particles from the bigger ones, a harmonic sum exists whether you break it up or not into its constituents. A hole in an opaque screen is a spatial filter producing a spherical oscillation analogously to an electric LC resonator that is a temporal filter outputting a near sinusoid temporal oscillation. Commented Mar 11, 2022 at 14:35
• Oh, which means that secondary wavefront is part of the wave, you need an opaque screen to separate them isn't it? Or if you saw a water wave why you can't see the secondary wavefront? If I'm wrong don't think I'm too stupid, I tried my best to understand it Commented Mar 12, 2022 at 1:12