鱼_鱼

Dispersion occurs because of the atomic structure of dielectric madia.

1. Let us just think of each atom as a single electron that osillates about a positive ion as if the electron were bound to that ion by a spring. Suppose the spring constant is given by (Omiga0)^2=k/m, where Omiga0 is the oscillation angular frequency. If no other forces are involved, the motion of the electron along the z-axis would then be of the form: z=A*cos(Omiga0*t)

2. Now consider that a plane electromagetic wave oscillating with angular frequency Omiga is incident on an atom, with electric field oriented in the z-direction. The situation is that of a driven harmonic oscillator. The amplitude of oscillation exhibits resonance when the two frequencies are close. Then the motion takes the form: z=1/((Omiga0)^2-(Omiga)^2)*cos(Omiga*t). For material like water and glass, Omiga0 is on the order of 5~6 times larger than the characteristic angular frequencies of visible light.

3. An accelerating eletron radiates electromagnetic energy and the intensity is proportional to a^2 and then proportional to (Omiga)^4

This is the result first obtained by Lord Rayleigh. We now use it to explain why the sky is blue.

p.s., 上面的字符都是我手写进去的.