Three polarizing plates whose planes are parallel are centered on a common axis.

Question

Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure below. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity 1,-10.5 units (arbitrary). Calculate the transmitted intensity If when | = 26.0°, 2 = 46.0°, and 3 = 58.0°. Hint: Make repeated use of Malus's law Step 1 When linearly polarized light of incident intensity Io passes through an analyzer whose transmission axis is rotated at angle to the plane of polarization of the incident light, the emerging light is linearly polarized in a direction parallel to the transmission axis of the analyzer. The intensity of the emerging light is given by Malus's law 1 = 10 cos2 The first analyzer in the figure has light of intensity I, incident on it. This light is polarized in the vertical plane. The light emerging from the first analyzer has intensity given by Malus's law as 11 = 1, cosag1 The transmission axis of the second analyzer in the figure is at angle = 2-0, from the plane of polarization of the light incident on it (the second analyzer). The intensity of light emerging from the second analyzer is 12 = 11 cos-e2-91) = 1, cosag1 cos2(82-91) The third analyzer has its transmission axis at angle = 3-2 from the plane of polarization of the light incident on it (the third analyzer). The intensity of the light emerging from the third analyzer is If = 12 cos-(93-92)-I, cosag1 cos2(92-81) cos2(93-82) If I, = 10.5 units, | = 26.0°, 2 = 46.0°, and 3-58.0°, the final emergent intensity of the light is given by the following If = 1, cos20, cos2(82-91) cos2(83-82) 10.5 unitsos(26.0°) cos2(20.0°) cos2 Your response differs from the correct answer by more than 100%

Explanation / Answer

angle between 1st and 2nd disk = 46.0 - 26.0 = 20.0 degree

angle between 2nd and 3rd disk = 58.0 - 46.0 = 12.0 degree

If = I1*cos^2(thetha 1) *cos^2(thetha 2-thetha 1)*cos^2(thetha 3-thetha 2)

= 10.5*cos^2(26.0)*cos^2(20)*cos^2(12.0)

= 10.5*0.808*0.883*0.957

= 7.17 units

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