Simple Nature - Light and Matter

ight side consists of a superposition of the incident wave consistingof E 0 and B 0 with a secondary wave E ∗ and B ∗ generated by theoscillating charges in the glass. Since the frequency is far belowresonance, the response qx of a vibrating charge q is in phase withthe driving force E 0 . The current is the derivative of this quantity,and therefore 90 degrees ahead of it in phase. The magnetic fieldgenerated by a sheet of current has been analyzed in subsection11.2.1, and the result, shown in figure e on p. 664, is just whatwe would expect from the right-hand rule. We find, t/1, that thesecondary wave is 90 degrees ahead of the incident one in phase.The incident wave still exists on the right side of the sheet, but it issuperposed with the secondary one. Their addition is shown in t/2using the complex number representation introduced in subsection10.5.7. The superposition of the two fields lags behind the incidentwave, which is the effect we would expect if the wave had traveledmore slowly through the glass.In the case f ≫ 0, the same analysis applies except that thephase of the secondary wave is reversed. The transmitted waveis advanced rather than retarded in phase. This explains the dipobserved in figure s after each spike.All of this is in accord with our understanding of relativity, ch. 7,in which we saw that the universal speed c was to be understood fundamentallyas a conversion factor between the units used to measuretime and space — not as the speed of light. Since c isn’t defined asthe speed of light, it’s of no fundamental importance whether lighthas a different speed in matter than it does in vacuum. In fact, thepicture we’ve built up here is one in which all of our electromagneticwaves travel at c; propagation at some other speed is only what appearsto happen because of the superposition of the (E 0 , B 0 ) and(E ∗ , B ∗ ) waves, both of which move at c.But it is worrisome that at the frequencies where n < 1, thespeed of the wave is greater than c. According to special relativity,information is never supposed to be transmitted at speeds greaterthan c, since this would produce situations in which a signal couldbe received before it was transmitted! This difficulty is resolvedin subsection 13.3.2, where we show that there are two differentvelocities that can be defined for a wave in a dispersive medium,the phase velocity and the group velocity. The group velocity is thevelocity at which information is transmitted, and it is always lessthan c.t / 1. A wave incident on asheet of glass excites current inthe glass, which produce a secondarywave. 2. The secondarywave superposes with the originalwave, as represented in thecomplex-number representationintroduced in subsection 10.5.7.Section 12.4 Refraction 781