It seems that I have been stuck on this one paragraph about the derivation of the law of reflection using Huygens' Principle. This is what I think I understand:
The line segment AA’ of the wavefront approaches the surface towards the lower right. As its lower tip hits the surface, it “activates” wavelets centered on the point where the line segment hits the surface. First activation is at point A. Since the point where line segment AA’ intersects with the surface is continuously moving to the right, more and more wavelets are being “activated” to the right until the line segment hits point O. At this instant, the first activated wavelet (the one centered at point A) has a radius equal to the perpendicular initial distance of line segment AA’ and the surface. Drawing a line tangent to all activated circles gives us the new reflected wavefront. By simple geometry, one can prove that the incident angle is equal to the reflected angle.
The problem is that I could not see this explanation in the paragraph. Is my understanding correct? Have I completely misunderstood its explanation? Or was it a different approach? I could not even see the “activated” wavelets on the figure. On the first sentence of the second paragraph, what does it even mean to change the direction?