Huygens Principle

In this lesson lets try to examine on Huygens Principle. Before we start lets try to know
" What is Huygens Principle?"
Huygens’ Principle (HP) contains both the principle of action-at-proximity and the superposition principle of waves . Although the propagation of sharp, non-spreading wave fronts is included in Huygens’ original formulation, it can be left out without touching those principles

We would first define a wavefront along with the wave theory : when we drop a small stone on a calmpool of water, waves spread out from the point of impact. Every point on
the surface starts oscillating with time.

If we have a point source emitting waves uniformly in all directions,
then the locus of points which have the same amplitude and vibrate in
the same phase are spheres and we have what is known as a spherical
wave as shown in Fig. At a large distance from the source, a small portion of the sphere can be considered as a plane and we have
what is known as a plane wave

Now, if we know the shape of the wavefront at t = 0, then Huygens
principle allows us to determine the shape of the wavefront at a later
time τ. Thus, Huygens principle is essentially a geometrical construction, which given the shape of the wavefront at any time allows us to determine the shape of the wavefront at a later time. Let us consider a diverging wave and let F1F2 represent a portion of the spherical wavefront at t = 0