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  4. The nature of light
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1.7 Polarization  (Page 2/20)

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The Sun and many other light sources produce waves that have the electric fields in random directions ( [link] (a)). Such light is said to be unpolarized    , because it is composed of many waves with all possible directions of polarization. Polaroid materials—which were invented by the founder of the Polaroid Corporation, Edwin Land—act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. If we think of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave.

Figure a shows a slender blue arrow pointing out of the page and to the right that is labeled direction of ray. Eight red arrows emanate from a point on the ray and are labeled as vectors E. These arrows are all in a plane perpendicular to the ray and are uniformly distributed around the ray. They are labeled as representing a random polarization. In figure b, a similar but longer ray is shown with the same red arrows emanating from a point near the left end of the ray. Farther to the right on the same ray is a thin rectangle with six equally spaced vertical slits. This rectangle is labeled polarizing filter. A vertical double headed arrow on its surface is labeled axis. To the right of the filter, centered on the ray, is a single blue double headed arrow oriented vertically that is labeled E and direction of polarization.
The slender arrow represents a ray of unpolarized light. The bold arrows represent the direction of polarization of the individual waves composing the ray. (a) If the light is unpolarized, the arrows point in all directions. (b) A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction. The direction of polarization of an EM wave is defined to be the direction of its electric field.

[link] shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second filter. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second filter.

This figure shows three illustrations of randomly polarized light passing through two polarizing filters, one after the other, in various orientations. In figure a, the two filters have axes oriented parallel to each other, in b the axis of the second filter is at an intermediate angle, between zero and ninety degrees, to the first’s, and in c the axis of the second filter is perpendicular to the first’s. Figure d is a photograph of the actual result of the first (parallel) and last (perpendicular) arrangements. In all the arrangements, the source light is randomly polarized, indicated by vector E arrows pointing in every direction in a plane perpendicular to the direction of propagation of the ray. In all the arrangements, the light that passed through the first filter, whose axis is oriented vertically, is vertically polarized, indicated by E vector arrows that only point vertically up and down. In figure a, all of the polarized light is passed by the second polarizing filter, whose axis is parallel to the first, and is still vertically polarized. In figure b, only some of the light is passed by the second polarizing filter, whose axis is tilted relative to the first. The light that passed the second filter is polarized in the direction of the second filter’s axis, and the magnitude of E is reduced. In figure c, where the filter axes are perpendicular to each other, none of the light passes through the second filter. Figure c shows a photo of three circular optical filters placed over a bright colorful pattern. Two of these filters are place next to each other and the third is placed on top of the other two so that the center of the third is at the point where the edges of the two filters underneath touch. Some light passes through where the upper filter overlaps the left-hand underneath filter. No light passes through where the upper filter overlaps the right-hand lower filter.
The effect of rotating two polarizing filters, where the first polarizes the light. (a) All of the polarized light is passed by the second polarizing filter, because its axis is parallel to the first. (b) As the second filter is rotated, only part of the light is passed. (c) When the second filter is perpendicular to the first, no light is passed. (d) In this photograph, a polarizing filter is placed above two others. Its axis is perpendicular to the filter on the right (dark area) and parallel to the filter on the left (lighter area). (credit d: modification of work by P.P. Urone)

Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ . If the electric field has an amplitude E , then the transmitted part of the wave has an amplitude E cos θ ( [link] ). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by

I = I 0 cos 2 θ

where I 0 is the intensity of the polarized wave before passing through the filter. This equation is known as Malus’s law    .

This figure provides additional details to the schematics of the two previous figures. In this figure, only one of the E vectors of the randomly polarized source light are shown to the left of the vertically oriented polarizing filter, along with the component of that vector parallel to the filter. The vector E is at an angle of theta to the vertical. The vertical component of the E vector is E cosine theta. After passing through the filter, the light has only vertical E, with magnitude E cosine theta.
A polarizing filter transmits only the component of the wave parallel to its axis, reducing the intensity of any light not polarized parallel to its axis.
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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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