This problem deals with combinations of ideal polarizing filters that have the net effect, first of polarizing incident light, and then of rotating the plane of polarization by 90°. In the text it was shown that two crossed polarizing filters (at 90° to each other) completely block initially unpolarized light that falls on the pair of filters. The first filter linearly polarizes the incoming light, resulting in an initially polarized intensity of Ip. Then the second crossed filter blocks all of the now-polarized light, and 0% intensity is transmitted. Somewhat surprisingly, adding a third filter between the crossed filters, so that each polarizer is rotated 45° with respect to the one just before it, does transmit some light. Again, the first filter linearly polarizes the incoming light, but the other filters cumulatively rotate this plane of polarization by 90° without blocking all of the light. In this case Ifinal = 0.25Ip, so 25.0% of the intensity emerging from the initial polarizer is transmitted through all three filters.
A combination of four filters, each rotated 30.0° clockwise with respect to the previous one, is exposed to light. This combination results in a 90° clockwise rotation of the plane of polarization that emerges from the first of the filters. What fraction of this initially polarized intensity Ip is the final intensity of the polarized light that emerges after passing through the other filters? Express your answer in terms of a percentage of Ip.


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