CHAPTER 8. Polarization Microscopy1. What is Polarized Light?Unpolarized light can be considered to be a collection of sinusoidal waves of the same amplitude all propagating in the same direction. In unpolarized light, all the azimuths of vibrationare represented equally, and in end view, the light looks like A or B.If the light is polarized, all the azimuths of vibration are not represented equally. In partially polarized light, some azimuths are represented less than others, or put another way the amplitude of some of the waves is less than the amplitude of other waves and in end view the light may look like D. In fully polarized light, the sinusoidal oscillations move in a three dimensional orientation, which when viewed from the end would appear as an ellipse. That is, fully polarized light can be considered to be elliptically polarized light that travels in three dimensions (G). In the special case, where the minor axis and major axis of the ellipse are equal, it is called circularly polarized light (F). In another special case where the minor axis of the ellipse equals zero, the light is linearly polarized (C,E). This is the form we usually use to illuminate an object in microscopy.In order to help us understand the various kinds of polarized light we can use a rope. One person holds the rope still and the other person moves his or her hand up and down in a straight vertical line.The wave generated moves from one person’s hand to the other person’s hand. The energy in the wave causes each point of the rope to move up and down. While the wave moves from one person to the other, the rope does not move sideways, but only moves up and down. This is a linear polarized wave whose azimuth of polarization is vertical.192If the second person moves his or her hand back and forth horizontally, the energy in the wave will cause each point of the rope to move from side to side. This is a linear polarized wave whose azimuth of polarization is horizontal or orthogonal to the vertically polarized wave. If both people move their hands with equal amplitude at the same time, one vertically, and the other horizontally, a spiraling motion will move down the rope, and each point of the ropewill move in a circular motion. We can “decompose” this wave by looking at the shadow of this "circularly polarized" rope wave on the vertical wall. It will look just like the vertically polarized wave. Now look at the shadow on the horizontal floor. It will look just like the horizontally polarized wave. We can consider the circularly polarized waves to be a combination of two linearly polarized waves. Elliptically polarized light is also a combination of two linearly polarized waves, except the amplitude of the up and down motion is different than the amplitude of the side to side motion. Here is an apparatus designed by Professor Wheatstone to demonstrate the interaction of two orthogonal linearly polarized waves (Pereira, 1854):Only transverse waves can be radially polarized. Thus light must be composed of transverse waves. This does not preclude the existence of longitudinal waves along with the transverse waves. By contrast, sound waves have only longitudinal and no transverse components. There is currently no satisfactory explanation of what is polarized light in terms of quantum theory (Dirac, 1958; Shurcliff and Ballard, 1964; Kliger et al., 1990; Allen et al., 1992; Collett, 1992; Georgi, 1993; Leach et al., 2002; Padgett et al., 2004). 2. Use an Analyzer to Test for Polarized LightWe can test whether or not light is linearly polarized by using an analyzer. One such analyzer is tourmaline, a colorful precious gem (Biot, 18**). Tourmaline is considered to be “dichroic”, since it absorbs certain wavelengths of light vibrating in one direction but not in another (Brewster, 1833). Consequently, the color of tourmaline depends on the azimuth of the incoming light. The same is true for sapphires and rubies (Pye, 2001). In one azimuth of polarization, sapphires pass only blue light while they pass white light in all other azimuths. Similarly rubies pass red light in one azimuth and white light in all others. Edwin Land developed193a crystal, known as a “Polaroid” which has the ability to absorb preferentially all the wavelengths of visible light that are vibrating in a certain azimuth. Light that is vibrating orthogonally to this azimuth is transmitted by the polaroid. Light that is vibrating at any other angle is transmitted according to the following relation:I = Io sin2where I is the transmitted intensity, Io is the incident intensity, and  is the angle between the azimuth of absorption and the azimuth of the incident light. Thus, if the intensity of light transmitted through the analyzer varies according to the above relation as one turns the analyzer, then the incident light is linearly polarized.Land made polaroids (of the J type) out of Herapathite or sulphate of iodo-quinine crystals embedded in cellulose acetate. Herapathite was serendipitously discovered by the physician William Bird Herapath when his student, Mr. Phelps noticed that, when he added iodineto the urine of a dog that had been fed quinine, a drug used to treat malaria, little scintillating green crystals appeared. Herapath looked at the crystals in a microscope and noticed they were light or dark in some places where they overlapped and realized that they had discovered a new dichroic material (Herapath, 1852; Herschel, 1876; Grabau, 1938; Land, 1951). Land, while an undergraduate student at Harvard University, read the second edition of David Brewster’s (1858) book on the kaleidoscope, in which Brewster dreamed of making plates of Herapathite that were large enough and strong enough to put on a kaleidoscope in order to produce beautiful interference colors from transparent crystals (see below), instead of the absorption colors produced by colored glass. Large flat herapathite crystals were too brittle. Land had the idea of embedding millions of tiny crystals of Herapathite in a gelatin medium. The medium was then subjected to stress in order to align the crystals so that their axes of maximal absorption were all co-aligned. The H type sheets that we use are made totally from man made crystals that are aligned by stress.Land (1951) wrote about his motivation in his own words: "Herapath's work caught the attention of Sir David Brewster, who was working in those happy days on the kaleidoscope. Brewster