Huygens Wavelets at an Optical Interface This animation will show the application of Huygens wavelets to an atomistic description of what happens at an iterface between the vacuum and a highly reflective curved mirror. In this way we can show how Snell's law of reflection derives from interaction between the wavelets and the oscillators that they excite in the mirror. Huygens wavelets are always circular in 2D or spherical in 3D. They just expand at the speed of light and have no phase information. For this animation, however, to avoid confusion and to keep the animation from running too slow, the wavelets will be shown as narrow arcs pointing in directions that will tend to result in focused radiation. I also represent the source (on the left) as a chosen number of dipole radiators where the dipoles are perpendicular to the plane of the screen. When the wavefronts arrive at the mirror, the dipoles in the mirror are excited at the same phase as the incident wavefronts and re-radiate similar wavefronts toward the chosen axis crossing position. For this animation, I have added phase information to the wavelets so that the learner can see how certain mirror axis crossing positions result in having the wavelets from all across the mirror being in phase which results in constructive interference and high intensity on the sxis. The phase information is in the form of colored wavefronts where red represents phases of 2npi and black represents phases of (2n+1)pi. It turns out that the best constructive interference for a spherical mirror occurs at an axial location of R/2 from the center of curvature of the mirror where R is its radius of curvature. At other axial locations the learner can see that the red and black wavefronts tend to coicide which represents destructive interference. Since reflection to an axial position R/2 is a result of the angle of reflection equaling the angle of incidence, these facts are a statement of Snell's law of reflection. The variation of the pathlength, ds, due to different ray heights on the mirror is plotted in blue versus the mirror height location. when this variation is equal to one half of a wavelength, then the wavelets from that height interfere destructively and the radiation from that part is zero. The learner should note that the phase (color) of the dipoles on the mirror surface moves inward as the source wavelets excite them.
mirrDiam mRad nDipoles dPhi xCross Single Step