I have seen the following illustration online and had a brief lecture about Huygens principle. As far as I understood, it suggests that every point in a wavelet acts like a point source to wavelets, which explains many phenomena.
However how do we treat the recursion here? If this is a general rule, after the infinitesimal time has passed, the generated wavelets should also behave like point sources and so on. Is this actually the case? And do we have a nice approach to it? Or are we just saying Huygens principle applies some times (when light changes medium or does interference pattern) and we do not comment this principle the other times? In other words, is this a sort of physical law that happens every instant, or a trick that holds from time to time and makes it easier to calculate?