41.55° angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce the intensity to 0.56 times the original intensity.
Assume that Io is the initial intensity and that is the angle between the polarizer and the filter axis.
After filtering, light has a 0.56 Io light intensity.
According to Malus's law, the amount of plane-polarized light that enters the analyzer is directly inversely proportional to the square of the cosine of the angle between the polarizer's plane and its transmission axis.
By applying the Malus law,
[tex]I = I_{0} Cos^{2}[/tex]θ
[tex]0.56I_{0} = I_{0} Cos^{2}[/tex]θ
[tex]0.56= Cos^{2}[/tex]θ
θ = 41.55°
Therefore, 41.55° angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce the intensity to 0.56 times the original intensity.
Learn more about Malus law here;
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