I'm not sure if I dare slightly disagree with Michelles excellent explanation, Michelles expertise in far greater than mine. However using a polarized filter agenised a grey sky will change the depth of the grey detail in the clouds, this will, be more apparent if there are a range or grey in a detailed cloudy sky, agenised a flat grey sky it will be more difficult to see. That said I have only ever used a polarized filter with an SLR camera and it is much easier to see a difference when you turn the filter. Agenised a blue sky it is much easier to see the colour saturation change. This should also be apparent in the light metering of the camera with the exposure (f stop and or shutter speed depending on what shooting mode is set) changing.

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