of certain optical properties of polar bears: they are white under illumination by white light but black in the ultraviolet. Briefly, their explanation invokes total internal reflection within the individual hairs comprising the pelt: the real part of the hair refractive index increases with increasing frequency (normal dispersion), so that a greater fraction of UV than visible light is totally internally reflected. They claim that the hairs act as light pipes that are more effective in the UV than the visible at guiding light to the underlying skin where it is absorbed. We suggest that this explanation ignores one of the most salient features of the optical properties of pro-
teins, of which hair is an example, and totally disregards some of the well-known physics of multiple scattering. We therefore offer an alternative explanation, albeit more prosaic, which is compatible with the observations.
A pelt is a multiple-scattering particulate medium, the individual particles of which are hairs. A common feature of all such media is that they appear white under illumination by white light if they are optically thick and if the particles are weakly absorbing at visible wavelengths (i.e., 1 − ω0 « 1, where ω0 is the single-scattering albedo). Numerous examples of a rather ordinary sort immediately come to mind: snow, clouds, flour, crushed glass, glass beads, salt, milk, sugar, etc. All these media have properties in the aggregate that are not possessed by the individual particles, or grains. Single ice grains in snow, or single glass beads, for example, are transparent; they also scatter light very weakly in backward directions. However, a sufficiently thick collection of them is highly reflecting at all visible wavelengths. Although scattering by a single particle large compared with the wavelength is highly peaked in the forward direction, the ultimate effect of a series of many scattering events in a collection of such particles is to strongly reflect the incident light, provided that in each event the amount of light absorbed by a particle is small. That is to say, the particles individually scatter photons preferentially in the forward direction, but collectively scatter (reflect) them in the backward direction, provided that few photons are lost by absorption. (The optics of a single ice grain and multiple scattering in snow have been discussed in detail by Bohr en and Barkstrom2.)
Grojean et al. imply that the whiteness of polar bear pelts originates from the internal roughness of the hollow hairs. Roughness however is not essential: it is not necessary to invoke rough water droplets to explain the whiteness and high albedo of clouds. All that roughening particles—internally or externally—does is to decrease the asymmetry parameter (average cosine of the scattering angle) so that fewer of them are necessary for the collection to be reckoned as effectively optically thick; that is, an incident photon undergoes fewer scatterings and, hence, has less chance of being absorbed before reemerging from the medium. Note that the shape and size of the particles is of little importance to the gross properties of the collection: if enough nonabsorbing particles are heaped into a pile, it will appear white if the source of illumination is white.
We obtained a sample of polar bear pelt from a fly tier and made a few simple observations. A single hair was suspended in the beam from a He-Ne laser. Although scattering was observed in all directions, forward scattering dominated. In particular, a series of bright maxima (diffraction peaks) was observed near the forward direction. Thus, polar bear hairs are not fundamentally different from any other particle large compared with the wavelength.
The blackness of polar bear pelts under illumination by UV light can be explained readily by appealing to the variation with frequency of the imaginary (absorptive) part of the refractive index of hair rather than the real part. One of the major constituents of hair is keratin,3 a protein; a characteristic of proteins is that they tend to have strong UV absorption bands.4 Bendit and Ross5 measured the UV absorbance spectrum of very thin sections (4 µm) of solid keratin in the form of near-white horsetail hair (they do not state whether it is the horse that is white, the hair, or both). Absorbances in the near UV ranged from ~0.01 at 380 nm to ~0.1 at 300 nm. Grojean et al. give the diameters of polar bear hairs as 100-150 µm with lengths between 6 and 7 cm. The average chord length6 in a convex body of volume V and surface area S is 4V/S; thus, the average chord length in a long cylinder is
approximately its diameter. Over a 100-µm path length the fraction of light transmitted by horsetail keratin ranges from ~0.56 at 380 nm to ~0.003 at 300 nm. If we assume that the UV absorption coefficient of polar bear keratin is not vastly different from that of horsetail keratin, then it is difficult to escape the conclusion that polar bear pelts are black in the UV because of absorption. Even though particles with dimensions of several hundred microns or greater may appear nearly transparent, it does not take much absorption in a single particle for a collection of them to be black. Again, the properties of the collection are not the same as those of its members. A simple demonstration of this is obtained with obsidian chips (~1 mm): they are individually transparent but collectively black.
Without undertaking complicated radiative transfer calculations, we can understand pelt reflection better by appealing to a very simple model of a multiple scattering medium, a pile of identical parallel laminae, which allows us to concentrate on the essential physics without being encumbered with details. Radiation normally incident on this system is partly reflected and partly transmitted at each interface; on a single pass through a lamina a fraction t of transmitted radiation is not absorbed. If r is the reflectance of the lamina-air interface, the reflectance R1 and transmit-tance T1 of a single lamina are (assuming no interference)
For two laminae, the corresponding quantities are
the reflectances and transmittances of 2n laminae (n = 2, 3,...) are obtained from these expressions by successive doublings. A more detailed analysis of the lamina model has been given by Benford.7 We are interested in the reflectance R ∞ of an optically thick collection of laminae, which is a sufficient number so that adding another lamina does not appreciably change the reflectance. We take r to be 0.05, which is characteristic of many insulators at visible and UV wavelengths; t = 0.56 is the value appropriate to a 100-µm lamina of keratin at 380 nm, the UV wavelength of minimum absorption. R∞ for these values of r and t is ~0.086 and is obtained with fewer than 8 laminae. Even if the absorption coefficient at 380 nm of polar bear keratin is one-tenth that of horsetail keratin (t = 0.94), R ∞ is ~0.35 and is obtained with ~16 laminae. This simple model has been invoked not with the intention that it be used to calculate pelt reflectances, but to show that it does not require much absorption in the elements of a multiple scattering medium that is in some ways similar to pelts to give low reflectances. We therefore suggest that the UV blackness of polar bears is only what is to be expected of any collection of proteinaceous particles regardless of their shape and roughness.
We have pointed to experimental evidence and invoked a simple model which suggests that absorption is the mechanism for the UV blackness of polar bear pelts. By way of contrast, the required variation of the real part of the refractive index of polar bear hair necessary to provide the mechanism proposed by Grojean et al. is not supported by any experimental evidence. Ultimately, however, absorption as the mechanism of pelt blackness can be vindicated only by measurements similar to those of Bendit and Ross.
Grojean et al. have implied, although not explicitly stated, that strong UV absorption by polar bear pelts is to the bear's advantage. This begs the question: How much UV light is available in the polar bear's environment? About 7.3% of the solar irradiance spectrum outside the earth's atmosphere lies
in the wavelength interval shortward of 380 nm.8 If we take the solar constant to be 1380 W/m2, the UV irradiance is ~100 W/m2, which is the maximum amount of UV radiation available to the bear. However, a greater fraction of UV than visible radiation is scattered by air molecules and absorbed by ozone in the atmosphere. This is particularly true at high latitudes, where slant paths are long: Gates's calculations of direct solar radiation at sea level clearly show increased depletion of shorter wavelengths as the air mass (slant path) is increased for a fixed amount of ozone.9 Of course, part of the scattered direct radiation will ultimately reappear as diffuse radiation. But the diffuse irradiances measured by Kuhn10
in the Antarctic at 79°S provide clear experimental evidence that the UV is more strongly depleted with increasing air mass than the rest of the solar spectrum. The more ozone in the atmosphere, the less UV radiation at the surface of the earth, direct or diffuse. It is significant, therefore, that ozone levels are higher at polar latitudes than mid-latitudes.11 Moreover, the "maximum in the Southern Hemisphere is not as pronounced [as that in the Northern Hemisphere] and is present at a somewhat lower latitude".12 Therefore, the UV irradiances measured by Kuhn are likely to be higher than those at corresponding latitudes in the Northern Hemisphere.
If efficient utilization of UV radiation were a necessary element in the bear's strategy for survival in a cold environment, it would seem that winter provides the severest test; during the Arctic summer the bear is likely to be devising ways to keep cool. In the depths of the Arctic winter, when the sun is low or even well below the horizon, diffuse radiation is the major component of the global UV irradiance. Kuhn reports an UV (300−400-nm) diffuse irradiance of <1 W/m2 for an air mass of ~ 5 (sun elevation ≃ 10°). If the average blackbody temperature of ground and sky is 260 K (see Idso and Jackson13 for a discussion of thermal radiation from the atmosphere), the bear receives ~260 W/m2 of IR radiation from his surroundings. The insignificance of 1 W/m2 becomes evident when we note that it corresponds to a fluctuation of <0.25 from 260 K. Although the polar bear may utilize UV radiation very efficiently, by whatever mechanism, it appears to avail him little because he lives in an environment relatively impoverished of such radiation. This is never more true than at the time of year when an appreciable increment of additional energy might tilt his marginal existence, if such it is, toward the side of survival.
We are indebted to Alistair Fraser, John Olivero, and John Kirby-Smith for their penetrating comments, incisive criticism, and helpful suggestions. We must also thank Don Peterson for suggesting sources of polar bear hair, Carl Chelius for acting as a broker, and George Harvey for parting with a choice piece of polar bear pelt. This work was performed under the auspices of the U.S. Department of Energy.
References 1. R. E. Grojean, J. A. Sousa, and M. C. Henry, Appl. Opt. 19, 339
(1980). 2. C. F. Bohren and B. R. Barkstrom, J. Geophys. Res. 79, 4527
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New York, 1979), p. 107. 4. D. M. Kirschenbaum, Atlas of Protein Spectra in the Ultraviolet
and Visible Regions (Plenum, New York, 1972). 5. E. G. Bendit and D. Ross, Appl. Spectros. 15, 103 (1961). 6. K. M. Case, F. de Hoffmann, and G. Placzek, Introduction to the
Theory of Neutron Diffusion, Vol. 1 (Los Alamos Scientific Laboratory, Los Alamos, 1953), p. 21.
8. N. Robinson, Ed., Solar Radiation (Elsevier, Amsterdam, 1966), p. 2.
9. D. M. Gates, Science 151, 523 (1966). 10. M. Kuhn, "Spectral energy distribution in shortwave fluxes over
the East Antarctic Plateau," in Energy Fluxes Over Polar Surfaces, World Meteorological Organization Technical Note 129 (1971).
11. H. D. Holland, The Chemistry of the Atmosphere and the Oceans (Wiley-Interscience, New York, 1978), p. 300.
12. J. London, "The observed distribution and variations of total ozone," in Proceedings of the NATO Advanced Study Institute on Atmospheric Ozone: Its Variation and Human Influences, Algarve, Portugal, 1-13 Oct. 1979, Report No. FAA-EE-80-20.
13. S. B. Idso, and R. D. Jackson, J. Geophys. Res. 74, 5397 (1969).
