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 24° relative to the axis of polarization of the incident light, and that the transmission axis of each additional analyzer is rotated 24° 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 15% that striking the first polarizer?

Explanation / Answer

Io = intensity striking the first polarizer

If = intensity after passing the nth polarizer

intensity after passing the first polarizer is given as

I1 = Io /2

I2 = I1 Cos2 24

I3 = I2 Cos2 24

I4 = I3 Cos2 24

so

In = (Io/2) Cos(n-1) 24

given that :

In = 0.15 Io

so

0.15 Io = (Io/2) Cos(n-1) 24

n-1 = 13.32

n = 14.32

so 14 polarizing sheets

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