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Scattering and polarized light
Description: Rayleigh scattering and polarization due to it. Using polarizing filter one can use polarization of scattered light to enhance certain features of the sky.

The process of scattering of light by a molecule (Rayleigh scattering) is an important physical phenomenon. Instead of thinking of light simply bouncing off the molecule, one should think of scattering as an absorption followed by re-radiation of light.

The probability for the light to be scattered is proportional to the inverse of the wavelength to the fourth power, . This means that the shorter wavelengths (towards blue) get scattered more strongly than the longer wavelengths (towards 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) and in the evening you see mostly transmitted light (red). The clouds have higher concentration of water and ice droplets. This means that light gets re-scattered 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 due to the fact that the scattered light is partially polarized. The white light scattered from the clouds is unpolarized, due to the fact that the light scatters randomly, multiple times. The direction of its polarization becomes random and thus the light is unpolarized. This can be useful for making pretty photographs of the sky.

A photographer wants to take a picture of an interesting cloud formation, so she uses a polarizing filter (assume that she is looking at a part of the sky where the blue is totally polarized) to increase the ratio of the clouds' intensity to that of the blue sky.

Part A
How would the photographer use the polarizing filter to find out the direction of polarization of the light coming from the blue sky? Her only reference is the polarization axis of the filter.
 rotate the filter until the light's intensity is minimum; light's polarization is along filter's axisrotate the filter until the light's intensity is maximum; light's polarization is along filter's axis
Part B
Find the angle 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.
Part B.1 Find the intensity of light from the sky through the polarizing filter
What is the intensity of light from the blue sky after it passes through the photographer's polarizing filter with the polarizing axis at an angle to the direction of the light's polarization? The intensity of light from the sky before it passes through the filter is .
Hint B.1.a Hint not displayed
Hint B.1.b Hint not displayed