Light after a Polarizer Question

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To determine the angle between the axes of two polarizers that allows 37.5% of the initial intensity of unpolarized light (240 W/m²) to pass through, the first polarizer reduces the intensity by half, resulting in 120 W/m². The transmitted intensity after the second polarizer is set to be 0.375 times the initial intensity, leading to a calculation where I2 equals 0.75 times I1. By applying the equation I2 = I1 * cos²(θ), it is found that cos²(θ) equals 0.75, resulting in an angle of 30 degrees. The solution confirms that the calculations are correct and the angle needed is indeed 30 degrees.
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Homework Statement


Initially unpolarized light with an intensity of 240W/m2 is incident on a series of two polarizers. What should be the angle between to the axes of the two polarizers such that the transmitted intensity after the second polarizer is 37.5% of the incident one?


Homework Equations



I=I0cos2\theta



The Attempt at a Solution



I1=.5Iocos2\theta (unpolarized light is reduced by halve after the first polarizer)
this can also be written at 2I1=Io

We are given that I2=0.375I1
2I1=Io so I2 really equals 0.75I1

0.75I1 = I1cos2\theta
0.75=cos2\theta
\theta = 30 degrees

Did I do this correctly?
Thanks for all your help...
 
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