Suppose you have four ideal polarizing filters (ideal means that they obey Malu\

Question

Suppose you have four ideal polarizing filters (ideal means that they obey Malu's law exactly) in a stack. Let's label them A, B, C, and D, with unpolarized light incident on A and passing through B, C, and D in that order. When all the filters axes are aligned, the intensity of the light that exits that stack is I0 . Now, rotate the axis of A clockwise by 10 degrees, rotate the axis of C clockwise by 20 degrees, and rotate the axis of D counterclockwise by 10 degrees. By what factor is the intensity of the light passing through the stack reduced, compared to I0?

Please explain and use diagrams.

Explanation / Answer

Let initial intensity of unpolarised light be I'
Intensity after 1st polariser = I'/2
Intensity after 2nd, 3rd and 4th [aligned polarisers] = Io = I'/2
I' = 2Io ........... (1)

after the configuration is changed

Angle b/w A and B = 10 deg
Angle b/w B and C = 20 deg
Angle b/w C and D = 30 deg [ 20 deg clockwise, 10 deg anti clockwise]

Intensity after A = Io
Intensity after B = Iocos^2(10) = 0.9698Io
Intensity after C = 0.9698Iocos^2(20) = 0.856 Io
Intensity after D = 0.856Iocos^2(30) = 0.6422 Io

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