![]() In this context, these equations can't be derived from anything "deeper" (except for string theory which has its own wave equations in the fundamental equations, too – and they can't be derived from something deeper, and if they can, I must say "and so on").Īnother aspect is why the wave equation above implies the Hyugens principle. the Klein-Gordon equation for the Higgs field) at the fundamental level (with some extra non-linear terms). Such an equation may be defined from a mechanical model of the water as a continuum, or water as a collection of many atoms, and so on.Īt the end, the fundamental laws we know – the Standard Model of particle physics, for example – contain some wave equations (e.g. For example, if water has "bumps" on it, the equation says that there is a force that tries to "flatten" these bumps. One aspect of the intuition is to know why this equation is right for a given physical system. The second time derivative of the height of the water at a given place $(x,y,t)$ at time $t$ is equal to the Laplacian (the sum of second $x$-derivative and $y$-derivative) of the same height. Here, $c$ is the speed of the waves ("fundamental" physicists would think about the speed of light as the most well-known example of the equation). The best intuition is the well-defined mathematics underlying the concept. Now you block the plane wave except at a gap which is comparable to the wavelength, and in doing so you extract one of the spherical waves which was generating the plane wave. You've managed to generate a plane wave by coherently combining a bunch of point sources. In the water example this can be done by moving a large flat surface back and forth which creates an infinite number of point sources along its surface.ĭiffraction is the opposite of this. ![]() Generating a plane wave, such as you have at the input of your image, requires taking many of these point sources and exciting them coherently such that their individual spherical waves add up to form a plane wave travelling in one direction. As an example consider throwing a rock into a pond the outgoing waves are emitted equally in all directions. In physics all point sources, wave sources which are smaller than the wavelength, generate outgoing spherical waves. It would be better phrased as: Why is it possible to have plane waves? I think you are looking at the question in a slightly backwards way. ![]()
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