Waves emitted by a radio transmitter are usually linearly polarized. The vertical rod antennas that are used for cellular telephones in automobiles emit waves that, in a horizontal plane around the antenna, are polarized in the vertical direction (parallel to the antenna). Rooftop TV antennas have horizontal elements in the United States and vertical elements in Great Britain because the transmitted waves have different polarizations.
The situation is different for visible light. Light from ordinary sources, such as incandescent light bulbs and fluorescent light fixtures, is not polarized. The “antennas” that radiate light waves are the molecules that make up the sources. The waves emitted
by anyone molecule may be linearly polarized, like those from a radio antenna. But any actual light source contains a tremendous number of molecules with random orientations, so the emitted light is a random mixture of waves linearly polarized in all possible
transverse directions. Such light is called unpolarized light or natural light. To create polarized light from unpolarized atura1light requires a filter that is analogous to the slot for mechanical waves in Fig. 34-16c. Polarizing filters for electromagnetic waves have different details of construction, depending on the wavelength. For microwaves with a wavelength of a few centimeters, a good polarizer is an array of closely spaced, parallel conducting wires that are insulated from each other. (Think of a barbecue grill with the outer metal ring replaced by an insulating one.) Electrons are free to move along the length of the conducting wires and will do so in response to a wave whose E field is parallel to the wires. The resulting currents in the wires dissipate energy by [2R heating; the dissipated energy comes from the wave, so whatever wave passes through the grid is greatly reduced in amplitude. Waves with E oriented perpendicular to the wires pass through almost unaffected, since
electrons cannot move through the air between the wires. Hence a wave that passes through such a filter will be predominantly polarized in the direction perpendicular to the wires. The most common polarizing filter for visible light is a material known by the trade name Polaroid, widely used for sunglasses and polarizing filters for camera lenses. Developed originally by the American scientist Edwin H. Land, this material incorporates substances that have dichroism, a selective absorption in which one of the polarized components is absorbed much more strongly than the other (Fig. 34 -17). A Polaroid filter transmits 80% or more of the intensity of a wave that is polarized parallel
to a certain axis in the material, called the polarizing axis, but only I% or less for waves that are polarized perpendicular to this axis. In one type of Polaroid filter, longchain molecules within the filter are oriented with their axis perpendicular to the
polarizing axis; these molecules preferentially absorb light that is polarized along their length, much like the conducting wires in a polarizing filter for microwaves. An ideal polarizing filter (polarizer) passes 100% of the incident light that is polarized in ‘the direction of the filter’s polarizing axis but completely blocks all light that is polarized perpendicular to this axis. Such a device is an unattainable idealization, but the concept is useful in clarifying the basic ideas. In the following discussion we will assume that all polarizing filters are ideal. In Fig. 34-18, unpolarized light is inSident on a flat polarizing filter. The polarizing axis is represented by the blue line. The E vector of the incident wave can be represented in terms of components parallel and
perpendicular to the polarizer axis; only the component o~if ~ar~llel to the ~larizing axis is transmitted. Hence the light emerging from the polanzer IS linearly polanzed parallel to the polarizing axis. When unpolarized light is incident on an ideal polarizer as in Fig. 34-18, the intensity of the transmitted light is exactly half that of the incident unpolari~d light, no matter how the polarizing axis is oriented. Here’s why: We can resolve the E field of the incident wave into a component parallel to the polarizing axis and a component perpendicular to it. Because the incident light is a random mixture of all states of polarization, these two components are, on average, equal. The ideal polarizer transmits only the component that is parallel to the polarizing axis, so half the incident intensity is ~smitted.
What happens when the linearly polarized light emerging from a pol~zer .passesthrough a second polarizer, as in Fig. 34-197 Consider the general cas~ m which ~e polarizing axis of the second polarizer, or analyzer, makes an angle ~ With~e polan~- ing axis of the first polarizer. We can resolve the linearly ~la~1Zed light that IS transmitted by the first polarizer into two components, as shown in Fig. 34-19, one parallel and the other perpendicular to the axis of the analyzer. Only the parallel component, with amplitude E cas ¢, is transmitted by the analyzer. The transmitted intensity is greatest when ¢ = 0, and it is zero when polarizer and analyzer are crossed so that ¢ = ?Do. To determine the direction of polarization of the light transmitted by the first polanzer, rotate the analyzer until the photocell in Fig. 34-19 measures zero intensity; the polarization axis of the first polarizer is then perpendicular to that of the analyzer.
To find the transmitted intensity at intermediate values of the angle ¢, we recall from our energy discussion in Chapter 33 that the intensity of an electromagnetic wave is.proportional to the square of the amplitude of the wave (see Eq. (33-26». The ratio of transmitted to incident amplitude is cas ¢, so the ratio of transmitted to incident intensity is cos’ ¢. Thus the intensity of the light transmitted through the analyzer is where I is the maximum intensity of light transmitted (at ¢ = 0) and I is the amount
transmi~ at angle ¢. This relation, discovered experimentally by Etienne Louis Malus in 1809, is called Malus’s law. Malus’s law applies only if the incident light passing through the analyzer is already linearly polarized.