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Polarized light is incident on three polarizing filters in a row. The initial intensity of the light is 4 W/m^2. The first filter is aligned vertically, the second at an angle of 45 degrees from vertical, and the third at an angle of 90 degrees from vertical. Afterwards the intensity is 0.5 W/m^2. At what angle relative to the vertical was the light initially polarized (give your answer as an angle between 0 and 90 degrees)?

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Answer:

45°

Explanation:

I = Polarized light after 3 filter = 0.5 W/m²

[tex]I_0[/tex] = Initial light intensity = 4 W/m²

The intensity of polarized light is given by

[tex]I=I_0cos^2Acos^245cos^245\\\Rightarrow A=cos^{-1}\sqrt{\dfrac{I}{I_0cos^245cos^245}}\\\Rightarrow A=cos^{-1}\sqrt{\dfrac{0.5}{4\times cos^245\times cos^245}}\\\Rightarrow A=45^{\circ}[/tex]

Hence, the angle relative to the vertical was the light initially polarized is 45°

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