Why is Huygens principle valid?
I think the answer is “because it works- it successfully describes nature”, which is basically the answer to all similar questions about physical principles we employ. The game in physics is to find the simplest possible descriptions that work, i.e. that lead to predictions that match observation. Huygens’ principle is the idea that each point on a wavefront can be considered a new source of waves, and creates a “wavelet” that spreads out and interferes with other wavelets. This has turned out to be an extremely useful, predictive idea, although it’s not the only way of thinking about things (we will not go beyond in this course, though).