You have a source of polarized light, and you send a beam of this light with int

Question

You have a source of polarized light, and you send a beam of this light with intensity I_0. through a number of polarizing filters. The first filter's polarization axis is rotated an angle theta clockwise (as viewed from the light source) from the original polarization axis of the light. Similarly, each successive filter's polarization axis is rotated an additional angle theta clockwise from the axis of the preceding filter. You want the light, after passing through all the filters, to have a polarization axis that is rotated a total of 29.7 degree from the polarization axis of the original light before passing through the filters, and to have been reduced in intensity by no more than 2.95% from its original intensity I_0. What is the minimum number of polarizers needed for this to occur? (Enter a whole number).

Explanation / Answer

After passing through first polarizer intensity will be

I1 = I0/2

After passing through second polarizer intensity will be

I2 = I1*(cos A)^2

I2 = (I0/2)*(cos A)^2

A = Angle between first and second polarizers

then it will continue like this for all the next polarizer,

In = (I0/2)*(cos A)2n - 2

given that

A = 29.7 deg

In = 2.95% of I0

In = 0.0295*I0

0.0295*I0 = (I0/2)*(cos 29.7 deg)^(2n - 2)

0.8686^(2n - 2) = 0.0295*2 = 0.059

(2n - 2)*ln 0.8686 = ln 0.059

n = (1/2)*[2 + (ln 0.059)/(ln 0.8686)] = 11.04

n = 11 polarizers

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