How Does Light Intensity Change Through Three Stacked Polarizing Films?

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When three perfect polarizing films are stacked with each oriented at +45 degrees relative to the previous one, the intensity of light passing through can be calculated using the Law of Malus. The initial light intensity of 1 watt will be reduced by the first polarizer to 0.5 watts, as it allows half of the light to pass through at a 0-degree angle. The second polarizer, oriented at 45 degrees, further reduces the intensity to approximately 0.25 watts. Finally, the third polarizer, oriented at 90 degrees, allows another reduction, resulting in an overall transmitted intensity of about 0.125 watts. Understanding these principles is crucial for analyzing light behavior through multiple polarizers.
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If you have 3 perfect polarizing films and you place them on top of the other, with each successive film oriented +45 degrees from the one before it (first and last oriented perpendicular to each other and middle polarizer at 45 degrees between them). If one shines a light on this polarizer stack with an intensity of 1 watt, what is the intensity of the light on the other side of the three polarizer stack?

Now when I tried to figure this out I assume that the light is collimated and that the films are perfect polarizer. But I got stuck on the actually equation... Anyone out there knows how to solve this?
 
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Perhaps the Law of Malus applies.

For each polarizer - Itrans = Io cos2\theta, where \theta is the angle of between axis of polarizer and some reference.

The question is what is the transmission of light through the first polarizer.

Edit: See http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polcross.html

for discussion of crossed polarizers and Law of Malus.
 
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