Animation of Concave Mirror Reflection Please click the link below for a description of the graphics. Rather than showing the reflected RAYS that follow Snell's law of reflection, here we show incident and reflected WAVES that don't always follow Snell's law but do intercept the mirror axis at a distance chosen by the "Test Focal Length" slider. The reason for this is that any of the oscillating charges at the mirror surface can and DO emit in a wide variety of angles but only the emissions at the angles given by Snell's law result in coherent addition of the phases at the mirror axis. In the case of a concave mirror, the axial position where the coherent addition takes place is a distance of r/2 from the center of the mirror and that is what is shown here where r is the radius of curvature of the mirror surface. This animation shows microscopic details of the incident wave, reflecting electron motion, and the exiting wave. The waves are depicted by sinusoid variation of electric fields and the electrons at the mirror surface move in synchronism with the incident wave. As shown in the Skin Effect article, for visible frequencies and a good conductive metal, only the electrons within about 0.1 micrometers of the surface are involved in the reflection process so it is reasonable to depict just the surface electrons. Note that the surface positive charge displacements (red) move inward toward the center of the mirror as the wave proceeds. That is just the movement of the tangential component of the incident wave vector which follows from Snell's law which states that the tangential component of the incident wave vector is continuous at the interface. Also note that the reflected waves crossing the mirror axis are very incoherent when the Test Focal Length is chosen to be far from 1/2 the radius of curvature of the mirror. At each new slider setting and at startup, I've also plotted the Focal Intensity versus wave crossing positions on the axis of the mirror. The vertical line is at distance r/2 from the center of the mirror and the peak of the focal intensity is generally very close to this line. In order to make the Focal Intensity distribution very narrow we must have very short wavelengths as well as a large number of waves. Both of these requirements cause the animation to run much slower so the startup parameter set is a compromise.
Click here for Skin Effect article Click here Focal Length Calculation Click here Graphics Description fNo rad fLen nRays dPhi