Three ideal polarizing filters are stacked, with the polarizing axis of the seco

Question

Three ideal polarizing filters are stacked, with the polarizing axis of the second and third filters at 21 degrees and 61 degrees, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 60.0 w/cm^2 after it passes through the stack. If the incident intensity is kept constant:

1) What is the intensity of the light after it has passed through the stack if the second polarizer is removed?

2) What is the intensity of the light after it has passed through the stack if the third polarizer is removed?

Explanation / Answer

Let the Intensity of the unpolarized light be Io

Intensity through First Polrizer, = Io/2
Intensity through Second Polrizer, = Io/2 * cos^2(21)
Intensity through Third Polrizer, = Io/2 * cos^2(21) * cos^2(61-21)
60.0 = Io/2 * cos^2(21)*cos^2(40)
Io = 120.0/(cos^2(21)*cos^2(40))
Io = 234.6 w/cm^2

(1)
If 2nd Polarizer is removed.
Intensity through Stack, = Io/2 * cos^2(61)
Intensity through Stack, = 234.6/2 * cos^2(61)
Intensity through Stack, = 27.6 w/cm^2

(2)
If 3rd Polarizer is removed.
Intensity through Stack, = Io/2 * cos^2(21)
Intensity through Stack, = 234.6/2 * cos^2(21)
Intensity through Stack, = 102.2 w/cm^2

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