The Blue Sky or Rayleigh Scattering
（Intro. PS、晴れた空はなぜ青い？これはハーシェルよりずっと後にたてられた問いだが、説明の追究が意外な成果をもたらすことの好例）
The following remark by Bohr (first paper, p. 27-8) may seem to have nothing to do with quantum mechanics, but it clearly shows the unexpected power of physics, and plain facts of ordinary life may lead to the discovery of the hidden structure of the nature.
Just as in the kinetic theory of gases, it is not merely the average effect of a large number of atoms that comes into consideration in the electromagnetic interpretation of optical phenomena. Thus, in the scattering of light the random distribution of the atoms makes the effects of the individual atoms appear in such a way that a direct counting of the atoms is possible. In fact, Rayleigh estimated from the intensity of the scattered blue light of the sky the number of atoms in the atmosphere, obtaining results in satisfactory agreement with the counting of atoms obtained by Perrin from a study of the Brownian motion.
Do you know why the sky is blue on a sunny day? This is because of Rayleigh Scattering; it is scattering of light by means of tiny objects (its size is smaller than the wavelength of the light in question). In view of the fact that scattering of alpha particles, of X-rays, and of electrons, played a very important role in the formation of quantum mechanics, it may be quite instructive to review this Rayleigh Scattering. The following figure shows, intuitively, the reason why the sky is blue.
It is crucial here that molecules in the air are distributed randomly. With this assumption, you can infer the number of molecules in a unit volume of the air. For Perrin's work (referred to in the quotation), see, e.g., Avogadro Number and the Brownian Motion. Incidentally, here is the blue sky in Oviedo, Spain, and myself representing Red and Blue Waves!
References
Bohr, N. Atomic Theory and the Description of Nature
Tomonaga, S. (1969) 量子力学 I、みすず書房。
