Scattering and Polarization

Scattering and Polarization C HAP T E R 13 13.1 these two molecules interferes de 1 3.2 INTRODUCTION structively. as in Figure 12.4 (along RAYLEIGH SCATTERING the x-axis). and this Is so for any - sideways direction from which you - So far we have considered what look at the beam. Air. on the other When white light scatters from hap pens when light encounters ma hand, is a gas. so there is no guar some molecules. it scatters selec terial obstacles of a size much antee that there will be another tively because part of the light is ab greater than the wavelength (geo molecule half a wavelength beyond sorbed at the resonant frequ encies metrical optics) or of a size so small the first-sometimes there may be a of the molecules-the scattered as to be comparable with the wave few extra molecules around one light Is then colored. For man y length of light (wave optics). But point, sometimes a few less. You see other molecules. however, the im you can also observe effects due the scattering from these pOints be portant resonant frequenCies are to even smaller obstacles, much cause of these fluctuations. (The significantly higher than visible fre smaller than the wavelength of visi TRY IT suggests ways to enhance quencies. White light nevertheless ble light. When light interacts with the scattering in air.) becomes colored when it scatters an isolated object that small, it Scattering is selective in several from these molecules-the higher shakes all the charges in the object, ways: light of certain wavelengths the frequency of the incident light. which th en radiate in all directions. is scattered more than light of other the more light will be scattered. This phenomenon is called scatter wavelengths. and light of one polar ThiS type of scattering is called ing. ization (Sec. 1.3B) is scattered Rayleigh scattering and occurs To scatter with appreciable inten more than light of another polari whenever the scattering particles sity, light must encounter many zation. Because our eyes are not are much smaller than the incident isolated small objects: for example, very sensitive to the polarization of wavelength and have resonances at the m olecules that constitute the light. we have not yet discussed the frequenCies higher than those of air. Indeed, it is onJy because light phenomena associated with it. visible light. Eq.uivalently, we may does scatter in air that you can Scattering provides us with the op write the rule for Rayleigh scatter see the beams of Figures 1.3, 1.4, portunity to do so, even as it ac ing: and 8.19b. Without scattering, the tually prOvides most of the polarized light's path through the air would light around us. Much of this chap The shorter the wavelength be invisible and the camera could ter will therefore deal with polarized of the incident light, the not record it. light, produced by scattering as well more light is scattered This simple explanation, offered as by other means. when these figu res were intro duced, now bears closer scrutiny. It This result was worked out in detail would seem that when propagating TR Y IT by the same Lord Rayleigh we met in any dense medium, such as in Sections 10.5B and 12.5C. It glass, light should be scattered by FOR SECTION 13.1 says that blue light will be scattered the many molecules that are pres Light beams more than red light. In fact, for in ent. Instead. as we know. it contin cident broad-band white light, the ues to propagate in a sharp beam, To see the path of light rays, you need intenSity of scattered 400-nm light as in vacuum, only with a different tiny objects in the path that will scatter Is almost ten times as great as that part of the light to your eye. To see the speed. This is because there are of 700-nm light. beam of your flashlight, put larger One consequence of Rayleigh scat many molecules present in glass, particles in the air, such as dust motes, and wh enever there is one molecule smoke, or chalk dust. In their presence tering is the sky's blue color. Light to scatter light, there will be an yo u should be able to trace the light's reaching your eyes from the sky is other one for which the light path path, including reflections from mirrors sunlight that has been scattered by to .your eye is half a wavelength and water surfaces, to test the law ofreflec the air molecules (Fig. 13.1 ) and is longer. The scattered light from tion (Sec. 2.4) and Snell's law (Sec. 2.5). therefore predominately blue. Since 347 CHAPTER I3, SCATTERING AND POLARIZATION 3 4 8 the direct rays from the sun have There are a number of other ex or sugar, talcum powder, ch alk , the some of the blue part of the spec amples where blue coloring is due white spots of moths and butter trtim scattered out of them they to Rayleigh scattering. We've al flies, white paper, fog, snow, beaten should look slightly yellowish. When ready noted (Sec. 9.9E) that fine egg white, and beer foam all look the sun is overhead, and if the sky black pigment mixed into white white for the same reason. The is very clear, this is a small effect. paint gives it a bluish cast for just white pattern in star rubies and However , if there are lots of tiny this reason. In fact, da Vinci noted sapphires, and in tiger's-eye quartz du st and smoke particles in the air, this and attributed it to the same are Similarly due to scattering from the effect is larger. It becomes even cause that makes the sky blue. The large inclusions. Likewise, the clear larger as the sun sets; the direct writer George MacDonald correctly albumen becomes white as an egg rays from it to your eyes must pass identifies another blue with the is cooked because the protein mol through more and more atmo blue of the sky when he writes, ecules are freed of their surface wa sphere, so these rays are depleted of "Where did you get those eyes so ter and are then able to coagulate more and more of the shorter wave blue?IOut of the sky as I came into large clumps, which scatter lengths, and the sun looks redder through." Your beautiful blue eyes nonselectively. When the watery and redder. (See the TRY IT.) are due to scattering from small, whey from milk is made into cheese widely separated particles in your (such as ricottal, the cheese is IrIses. Similarly, the moonstone white because of the same coagula owes its blue sheen to Rayleigh tion process. scattering. Yellow lights are often u sed as fog You can see the same effect in lights or headlights on cars because fine smoke, say from a wood fire. yellow is as easily detected by your The smoke looks bluish when illu eyes as white but is scattered less in minated from the side and viewed a fine mist, when the droplets are against a dark background, so only very small compared to the wave scattered light reaches your eyes. If length of visible light. Un fortu instead the smoke is seen against a nately, more often the droplets are bright background, it looks red or larger, and the yellow is then scat brown (due to the removal of blue tered as well. by scattering). If the smoke gets too Particles may, of course, also pro thick, the particles become dense duce colors by selective absorption enough that all light is repeat and r€iflection. The smog we all edly scattered, and the light that know and love takes its brown color emerges sideways is white or gra,y. because of absorption by particles A similar effect can occur when of nitrous oxide, which has reso the particles become larger. For ex nances at visible frequencies. Not ample, the smoke rising from the all particles in the sky produce ugly end of a Cigarette is bluish, but af colors, however. For example, in ter you inhale and exhale it, the 1883 the volcano Krakatoa erupted smoke looks gray or white. Here you spectacularly, spewing micrometer have covered the smoke particles size particles into the atmosphere with mOisture, making them much in such abundance that all over the larger. They are then large enough world there were unusually colorful to scatter light of all wavelengths sunrises and sunsets for three equally-as in the reflections of geo years! metrical optics-and thus they look Scattering by the air or the parti fiGURE 13.1 white. This is also why clouds are cles in it is thus responsible for aer white: The water droplets in clouds ial perspective (Sec. 8.6El, wh ich When A looks at point C in the sky, only scattered light from the sun reaches her may be fifty times as large as the makes distant dark hills look blue eyes. As short-wavelength light is wavelength of visible light. With so and distant snow-clad peaks look scattered most, the sky looks blue to many droplets, and thus so many yellow (see Plate 8.4). The purer and her. Direct rays from the sun, from surfaces to reflect the light, the more transparent the air, the bluer which the blue end of the spectrum has been removed by scattering, vary from clouds scatter almost all the light those dark hills.

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