Figure 5
From: Huygens' Principle geometric derivation and elimination of the wake and backward wave
Non expanding spherical shell impulsive source. (a) A spherical cap on an impulsive spherical shell source. (The spherical shell may be referred to as a 'sphere' hereafter.) The radius is R0, and the sphere is centered at the coordinate origin and has impulsive excitation δf (t). Each point on the sphere’s surface represents a point source which radiates an impulsive spherical wavelet. The parameter z0 is the radial distance from the sphere's surface to the point in space, P, at which the resultant wave field φ will be observed as a function of time. The propagation speed is c. The distance ct from P to a point on the sphere defines a spherical cap of height h(t) with radius R1. The sphere is transparent to radiation so that the whole sphere will contribute to the wave field at any one point in space. (b) The locus of all contributing radiating points is a spherical zone. These are the only points on the spherical source of radius R0 which can contribute to the field at P during the time interval [t, t + ε] and at distance z0 from the sphere. The zone on the spherical source is bounded by its intersection with two concentric spheres of radius ct and radius c[t − ε] centered at the field point P. The intersections defines spherical caps of heights h(t) and h(t + ε), also radii R1 and R2.
