Undergrad Huygens principle introduction

[abhinavjeet]

why only the common tangential surface of the secondary wavelets forms the new wavefront ?
what about all the other interferances that might occur between the waves of the secondary sources , like the constructive interferances that occur slightly offside towards the inside of the tangential surface but still have
not been canceled by destruactive interferance?

 

[mfb]

like the constructive interferances that occur slightly offside towards the inside of the tangential surface but still have
not been canceled by destruactive interferance?

There is no such thing, if you consider sufficiently large homogeneous areas. If you have very small surfaces or some patterns in the surface, you can get additional angles, this is the idea of diffraction.

 

[Joyal Babu]

First thing you need to realize is that huygens principle is just an analysis tool.It helps you find how the wave front will be at a later time if we are given the initial wave front.You can look into huygens paper on his principle where he have shown if we can consider each new point in space where the wavefront reaches as a new source which emits spherical wavefronts then we can construct the later wavefront as the one joining all the common tangential surface of the secondary wavelets

 

[vanhees71]

The Huygens principle is a heuristic way to approximately solve the (linear!) wave equation. The correct way is of course to use the corresponding retarded propagator. The first thing you learn is that it holds only in odd-dimensional spaces. E.g., in 2D-wave problems it's invalid!