The strong frequency dependence of the power formula is what accounts for the blueness of the sky. Sunlight passing through the atmosphere stimulates atoms to oscillate as tiny dipoles. The incident solar radiation covers a broad range of frequencies (white light), but the energy absorbed and reradiated by the atmospheric dipoles is stronger at the higher frequencies because of the ω^4 in Eq. 11.22. It is more intense in the blue, then, than in the red. It is this reradiated light that you see when you look up in the sky—unless, of course, you’re staring directly at the sun.
\left\langle P\right\rangle=\int{\left\langle\pmb{S}\right\rangle }.da=\frac{\mu _{0}P^{2}_{0}\omega ^{4}}{32\pi^{2}c}\int{\frac{\sin^{2}\theta}{r^{2}}r^{2}\sin\theta d\theta d\phi} =\frac{\mu _{0}P^{2}_{0}\omega ^{4}}{12\pi c}. (11.22)
