More than one analyzer can be used in a setup like that in the drawing, each ana

Question

More than one analyzer can be used in a setup like that in the drawing, each analyzer following the previous one. Suppose that the transmission axis of the first analyzer is rotated 25° relative to the transmission axis of the polarizer, and that the transmission axis of each additional analyzer is rotated 25° relative to the transmission axis of the previous one. What is the minimum number of analyzers needed for the light reaching the photocell to have an intensity that is reduced by at least a factor of 100 relative to that striking the first analyzer?

Explanation / Answer

From the Malus equation

I = Io cos^2 theta

log (I) = Iolog cos^2 theta

taking the common algorthemm

2N log ( cos theta ) = log ( 0.010)

2N log ( cos 25) = log (0.010)

N = log (0.010)/ 2 ( log cos 25)

=23

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