Why is the sky blue?
The dipole moment of the atom is directly proportional to the incident electric field
where is a complex constant called electrical polarizability. It follows that
(8)
The power of a wave is directly proportional to the square of its amplitude. The power of the light incident on the atom is
(9)
can be written in terms of the intensity of the incident light by (8) and (9)
Suppose a beam of light traverses a distance of by different atoms is assumed to have random phases and the total intensity of the light scattered per distance is and hits N atoms in the volume. Light scattered
Taking
to be infinitesimal,
N now becomes the number of molecules per unit volume. The solution is simply
Which fits the formula derived from macroscopic observations
Though this model works well for small and simple molecules, t apply to particles significantly larger than the wavelength of light which scatter all frequencies of light equally. 211 More complicated molecules are affected by their own internal dynamics which is not explored in this model. 212 here are some limits. It does not
We started with a simple question. The answer is a cascade of daunting mathematical formula. However the scientific ideas that underpin the maths are elegant. Atoms behave like springs. Light
tugs the springs and the atoms become trillions of tiny s illuminate the skies, but very much our imagination.
olar-powered bulbs. These bulbs not only
211 Rossing, Thomas D., and Christopher J. Chiaverina. ‘1.3 Why Clouds Visual Arts. New York: Springer, 1999. 5 212 Lipson, S. G., and H. Lipson. ‘13 The Classical Theory of Dispersion.’ Optical Physics. London: Cambridge U.P., 1969. 469-503. Print. are White.’Light Science: Physics and the -6. Print.
102
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