More than one analyzer can be used in a setup like that in thefollowing figure,

Question

More than one analyzer can be used in a setup like that in thefollowing figure, each analyzer following the previous one. Supposethat the transmission axis of the first analyzer is rotated 24°relative to the transmission axis of the polarizer, and that thetransmission axis of each additional analyzer is rotated 24°relative to the transmission axis of the previous one. What is theminimum number of analyzers needed, so the light reaching thephotocell has an intensity that is reduced by at least a factor ofone hundred relative to that striking the first analyzer?

Explanation / Answer

Malus' Law: I = I0cos2 I1 = I0cos2 I2 = I1cos2 =(I0cos2)cos2 =I0cos4 And so forth. You'll find that for n analyzers, the intensityis In = I0cos2n So for this problem, I0/100 = I0cos2n24 Solve for n. 10-2 = (cos 24)2n 10-1/n = cos 24 -1/n = log(cos 24)    [notice I'm using commonlogarithms, not natural logs] n = -1/log(cos 24) I get an answer of just over 25.

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