Simple Nature - Light and Matter

12.4.6 ⋆ Microscopic description of refractionGiven that the speed of light is different in different media, we’veseen two different explanations (on p. 774 and in subsection 12.4.5above) of why refraction must occur. What we haven’t yet explainedis why the speed of light does depend on the medium.s / Index of refraction of silicaglass, redrawn from Kitamura,Pilon, and Jonasz,Applied Optics 46 (2007)8118, reprinted online at http://www.seas.ucla.edu/~pilon/Publications/AO2007-1.pdf.A good clue as to what’s going on comes from the figure s. Therelatively minor variation of the index of refraction within the visiblespectrum was misleading. At certain specific frequencies, n exhibitswild swings in the positive and negative directions. After each suchswing, we reach a new, lower plateau on the graph. These frequenciesare resonances. For example, the visible part of the spectrumlies on the left-hand tail of a resonance at about 2 × 10 15 Hz, correspondingto the ultraviolet part of the spectrum. This resonancearises from the vibration of the electrons, which are bound to thenuclei as if by little springs. Because this resonance is narrow, theeffect on visible-light frequencies is relatively small, but it is strongerat the blue end of the spectrum than at the red end. Near each resonance,not only does the index of refraction fluctuate wildly, but theglass becomes nearly opaque; this is because the vibration becomesvery strong, causing energy to be dissipated as heat. The “staircase”effect is the same one visible in any resonance, e.g., figure kon p. 180: oscillators have a finite response for f ≪ f 0 , but theresponse approaches zero for f ≫ f 0 .So far, we have a qualitative explanation of the frequency-variationof the loosely defined “strength” of the glass’s effect on a light wave,but we haven’t explained why the effect is observed as a change inspeed, or why each resonance is an up-down swing rather than asingle positive peak. To understand these effects in more detail, weneed to consider the phase response of the oscillator. As shown inthe bottom panel of figure j on p. 181, the phase response reversesitself as we pass through a resonance.Suppose that a plane wave is normally incident on the left side ofa thin sheet of glass, t/1, at f ≪ f 0 . The light wave observed on the780 Chapter 12 Optics