The above diagram represents a series of polarizers. (six are shown, but it coul

Question

The above diagram represents a series of polarizers. (six are shown, but it could be fewer or more), each rotated through the same angle 0 = N, 37.9 with respect to the previous polarizer. Initially unpolarized light shines from the left. How many polarizers are necessary to get the final intensity of the light emerging on the right to be under 1/100 (that is, 1%) of the initial intensity of the unpolarized light? Answer: __________ polarizers How many polarizers are necessary to get the final intensity of the light emerging on the right to be under 1/1000 (that is, 0.1%) of the initial intensity of the unpolarized light? Answer: _____________ polarizers

Explanation / Answer

Given

   the angle of rotation for eacach polarizer is 37.9 degrees
we know that the intensity of polarized light is I1 - I0 cos^2 theta

   I1 = I0*cos^2(37.9) = 0.62265 I0

   I2 = 0.62265 I0*cos^2(37.9) = 0.38769 I0

I3= 0.38769 I0*cos^2(37.9) = 0.24140 I0

I4 = 0.24140I0*cos^2(37.9) = 0.15031 I0

I5 = 0.15031 I0 *cos^2(37.9) = 0.0939 I0

I6 = 0.0939 I0*cos^2(37.9) = 0.05827 I0

I7 = 0.05827 I0 *cos^2(37.9) = 0.036285 I0

I8 = 0.036285 I0 *cos^2(37.9) = 0.02259299 I0

I9 = 0.02259299 I0 *cos^2(37.9) = 0.0140676 I0

I10 = 0.0140676 I0*cos^2(37.9) = 0.0087592430908 I0

I11 = 0.0087592430908 I0 cos^2(37.9) = 0.0054539750578 I0

I12 = 0.0054539750578 I0*cos^2 37.9 = 0.0033959377109 I0

I13 = 0.0033959377109 I0*cos^2 37.9 = 0.0021144931567 I0

I14 = 0.0021144931567 I0*cos^ 37.9 = 0.0013165969727 I0

a)the number of polarizers required to get the intesity of the polarized light is of 1 % intensity is 9

b) the number of polarizers required to get the intesity of the polarized light is of 0.1 % intensity is 14

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