Polarizers 1 and 3 have their axes of polarization, indicated by the black solid

Question

Polarizers 1 and 3 have their axes of polarization, indicated by the black solid lines, perpendicular to each other. If you try to shine light through only the combination of 1 and 3, you will find that none passes through. However, now we put in another polarizer (number 2 in the figure) between number 1 and number 3. This polarizer has an axes of polarization that has an angle of 0 - 58 degree with respect to the polarization axes of polarizer 1. Surprisingly, now some light passes through the combination 1 + 2 3. What percentage of the initial (unpolarized) light intensity passes through?

Explanation / Answer

Intensity of light through polarizer2 I2 = I1*(cos58)^2 = (Io/2)*(cos58)^2

Intensity of light through polarizer 3 I3 = I2*(cos(90-58))^2

I3 = (I0/2)*(cos58)^2*(cos32)^2

I3/I0 = 0.101

percent = 10.1 %

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