The process of scattering of light by a molecule (rayleigh scattering) is an important physical phenomenon. instead of thinking of scattering as light simply bouncing off the molecule, one should think of it as an absorption followed by reradiation of light.

the probability for light to be scattered is proportional to the inverse of the wavelength to the fourth power, (1/λ^4). this means that the shorter wavelengths (toward blue) get scattered more strongly than the longer wavelengths (toward red).

rayleigh scattering can explain why the daytime sky looks blue, the sunset looks red, and clouds are white. in the afternoon you observe mostly scattered light (blue); in the evening you see mostly transmitted light (red). the clouds have higher concentration of water and ice droplets. this means that light gets rescattered many times and all wavelengths get a chance to scatter out of the clouds, adding up to white light.

another effect that can be explained by light scattering is polarization. when you look at the sky with polaroid sunglasses it appears darker or brighter from different angles. this is because the scattered light is partially polarized. the white light scattered from the clouds is unpolarized, because the light scatters randomly, multiple times. the direction of its polarization becomes random and thus the light is unpolarized. this effect can be useful for making dramatic photographs of the sky.

consider a photographer who wants to take a picture of an interesting cloud formation. to increase the ratio of the clouds' intensity to that of the blue sky the photographer uses a polarizing filter.

find the angle ϕ between the filter's polarizing axis and the direction of polarization of light necessary to increase the ratio of the clouds' intensity to that of the blue sky so that it is three times the normal value.

express your answer in degrees to four significant figures.