Explain why differnt optical media will have different refractive indices
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Refractive index describes the speed of propagation of light in a medium. So to restate your question:
why is the speed of light slower in some media than in others?
The wave equation tells us that speed of propagation depends on two factors: one is an inertial term, while the other is an elastic term. Let's look at a simple case of a string. The velocity of wave propagation in a string goes as
v=Tμ−−√v=Tμ
where TT is the tension, and μμ is the mass per unit length.
When light propagates in a dielectric medium, the electrons in that medium are moved by the EM field of the light. These moving electrons in turn emit an electromagnetic wave, but this wave will be lagging in phase with the signal that caused their motion.
Because of this phase lag, the combined signal that propagates is the sum of the initial signal (now a bit smaller because it gave some of its energy to the electron) plus the phase-shifted signal from the electron. Together, they create a phase shift in the original signal - it is as though it is going slower.
The shift due to one electron is tiny; but the more electrons you have per unit volume, the greater the effect will be. The actual force with which the electrons are bound (the "elastic constant" if you like) also comes into play, so you can't simply say that refractive index scales with density .....
why is the speed of light slower in some media than in others?
The wave equation tells us that speed of propagation depends on two factors: one is an inertial term, while the other is an elastic term. Let's look at a simple case of a string. The velocity of wave propagation in a string goes as
v=Tμ−−√v=Tμ
where TT is the tension, and μμ is the mass per unit length.
When light propagates in a dielectric medium, the electrons in that medium are moved by the EM field of the light. These moving electrons in turn emit an electromagnetic wave, but this wave will be lagging in phase with the signal that caused their motion.
Because of this phase lag, the combined signal that propagates is the sum of the initial signal (now a bit smaller because it gave some of its energy to the electron) plus the phase-shifted signal from the electron. Together, they create a phase shift in the original signal - it is as though it is going slower.
The shift due to one electron is tiny; but the more electrons you have per unit volume, the greater the effect will be. The actual force with which the electrons are bound (the "elastic constant" if you like) also comes into play, so you can't simply say that refractive index scales with density .....
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