Here's a brief analysis of the effect of a polarizer on the "blueness" of the sky. The fisheye photo was taken pointing straight up at susnset (sun on the right.) A polarizing filter was used with the polarizer aligned along the east-west axis (horizontal diameter).
The ImageJ graphs to the right of the photo are the red, green, and blue components of the light across the diameter of the photo (ie. from east to west). Compare the relative red, green & blue intensities at the peak on the left with that in the valley; there's a greater fraction of blue in the valley - ie. the sky is about 20% "bluer" as well as darker.
Dave
PS
This fisheye photograph (hi-res) of the full sky at sunset was kindly provided by Forrest Mims of electronics authoring fame. He took it from his South-Central Texas Observatory using a polarizing filter aligned East-West. The roughly North-South line of dark blue sky shows where polarization was at its maximum. As the title of that country-western song not yet written says: "the skies of Texas are bluest for the cowboy with sunglasses and no blues to sing."
Mims will grant use of this picture for noncommercial use by students and individuals so long as acknowledgment is given. If you are interested in computers, you should read his first-hand account of the history of Altair, the first commercial personal computer, at his site Forrest M. Mims III.
see:
The polarization of the sky Disclaimer I am no expert on these topics and the conclusions I offer are just observations based on
ad-hoc measurements of data drawn from whatever sources are handy. I avoid saying things I can't justify with actual measurements, but that doesn't guarantee correctness.
I've learned an awful lot doing these measurements/analyses; before this morning, I thought a polarizer's effect was to darken some of the sky, not to change its color! Amazing what can be discovered when one measures rather than assumes.