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When a circularly polarized light is incident on a linear polarizer, shouldn't the transmission of said light be dependent on the momentary orientation of the polarization at the instance of incident? Would that imply that the transmission should be dependent on the distance between the circular and linear polarizers?

The answer to that second question seems to be 'no' from some naive experiments I did, but I wonder why.

Is it because the that the momentary orientation of circular polarization is not spatially fixed, or is there some other explanation?

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Circularly polarized light can be written as the superposition of two orthogonal waves with linear polarization that are a quarter of a wavelength out of phase. Choose the direction in such a way that one is transmitted and the other one will be absorbed.

(I probably did not understand the question.)

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"shouldn't the transmission of said light be dependent on the momentary orientation of the polarization at the instance of incident" - the answer is yes, it is. But the instantaneous polarization in a specific point is space fluctuates in the frequency of the EM field, so at the end you get a linear polarized EM field with the same frequency as the original circular polarized light, as it should be.

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You are right this in thinking the intensity actually depends on direction of orientation with the polariser as by Malus' Law (I=I°(cos(x))^2) where x is angle. But the vector rotates so x varies.hence we find average value.Over an interval of one complete rotation avg value of (cosx)^2 is 0.5. So resultant intensity is half the incident intensity.

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