A polarized light is incident on several polarizing disks whose planes are paral

Question

A polarized light is incident on several polarizing disks whose planes are parallel and centred on common axis. Suppose that the transmission axis of the first polarizer is rotated 16° relative to the axis of polarization of the incident light, and that the transmission axis of each additional analyzer is rotated 16° relative to the transmission axis of the previous one. What is the minimum number of polarizer needed (whole number), so the transmitted light through all polarizing sheets has an intensity that is less than 20% that striking the first polarizer?

Explanation / Answer

here,

theta = 16 degree

the initial intensity be I0

final intensity , I = 0.2 * I0

let the number of polarizers be n

I = I0 * ( cos(theta))^2n

0.2 * I0 = I0 * ( cos(16))^2n

solving for n

n = 20.36

the minimum number of polarizers needed is 21

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