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 Ii = 14.0 units (arbitrary). Calculate the transmitted intensity If when 1 = 17.0°, 2 = 45.0°, and 3 = 55.0°. Hint:Make repeated use of Malus's law.
If =  units

Explanation / Answer

For the problem situation where you start with polarized light, each pass will reduce the intensity of the light by a factor of sin(theta), where theta is the angle between the current light polarization and the orientation of the polarizing filter.

I = Ii * sin( theta )

Filter 1:

The light is polarized vertically (so it's angle relative to the reference vertical is _light_init = 0° and the filter is align at an angle of 1 = 17°, so

I_f1 = Ii * cos^2( 1- _light_init) = 14 * cos^2(17-0) = 14 * 0.9145 = 12.8
Filter 2:
After passing through filter 1, the light now has a polarization parallel to the orientation of filter 1. This is the function of the filter, to allow only the portion of like that is aligned to it's orientation. So _light_1 = 1.

I_f2 = I_f1 * cos^2( 2 - _light_1) = 12.8 * cos^2( 45-17 ) = 9.98
Filter 3:
Now _light_2 = 2, so
I_f3 = I_f2 * cos^2( 3- _light_2) = 9.98* cos^2(55-45) = 9.679

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