A linearly polarized beam of light of intensity I 0 is propagating in the + z di
ID: 1451321 • Letter: A
Question
A linearly polarized beam of light of intensityI0 is propagating in the +z direction and its direction of polarization makes an angle of 75° with the x-axis (the angle between the initial direction of polarization and the transmission axis of the first polarizer is 15° as described below). Twolinear polarizing sheets are lined up perpendicular to the beam. Thefirst sheet has its transmission axis at an angle q 1 = 90° with respect to thex-axis. The transmission axis of the second is variable. (Seelower panels of the figure.)
(a) Calculate the intensity I1 of the light after ithas passed through the first polarizer. Express your answer as afraction of I0.
I1 / I0 =
(b) The second polarizer is set at various angles within the rangeq 2 = 0 to 90°.Calculate the intensity of the light after it has passed through thesecond polarizer for the following values of q 2. Express each answer as a fractionof I1.
At q 2 = 0°: I2 / I1 =
At q 2 = 32°: I2 / I1 =
At q 2 = 90°: I2 / I1 =
side vieu 8-90 : variable end iews 2Explanation / Answer
(a) Calculate the intensity I1 of the light after ithas passed through the first polarizer. Express your answer as afraction of I0.
I1 / I0 =
from Malus law
we can write, I1=I0 *cos2(theta)
I1/I0 = cos2(15) = 0.933
b) 1.The angle between the light incident on the second polarizer and the transmission axis of the second polarizer is (if I understand the problem correctly) (90° - q2).
The intensity of light transmitted by the second polarizer is then
I2 = I1 cos2(90° - q2) = I0 cos2(15°) cos2(90° - q2)
For q2 = 0°,
I2 / I0 = cos2(15°) cos2(90°)
I2 / I0 = 0
2.The angle between the light incident on the second polarizer and the transmission axis of the second polarizer is (if I understand the problem correctly) (90° - q2).
The intensity of light transmitted by the second polarizer is then
I2 = I1 cos2(90° - q2) = I0 cos2(32°) cos2(90° - q2)
For q2 = 32°,
I2 / I0 = cos2(32°) cos2(58°)
I2 / I0 = 0.2019
3.The angle between the light incident on the second polarizer and the transmission axis of the second polarizer is (if I understand the problem correctly) (90° - q2).
The intensity of light transmitted by the second polarizer is then
I2 = I1 cos2(90° - q2) = I0 cos2(90°) cos2(90° - q2)
For q2 = 90°,
I2 / I0 = cos2(90°) cos2(0°)
I2 / I0 = 0
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