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As vector wavefunctions are available to represent incident and scattered fields in an isotropic dielectric-magnetic medium endowed with magnetoelectric gyrotropy, a transition matrix can be conceptualized to relate the scattered field coefficients to the incident field coefficients for scattering by an arbitrary scatterer composed of a linear medium. The elements of the transition matrix must satisfy certain conditions for zero backscattering. For a scatterer composed of a uniaxial dielectric-magnetic medium endowed with magnetoelectric gyrotropy, the extended boundary condition method (EBCM) can be formulated to determine the transition matrix. The numerical results obtained thereby lead to the formulation of a sufficient set of three zero-backscattering conditions: (i) the scatterer is a body of revolution with the incident plane wave propagating along the axis of revolution; (ii) the impedances of both mediums are identical; and (iii) the magnetoelectric-gyrotropy vectors of both mediums are aligned along the axis of revolution, whether or not both magnetoelectric-gyrotropy vectors are co-parallel.

The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic when the constitutive principal axes are arbitrarily oriented with respect to the shape principal axes. Known vector spherical wave functions are used to represent the fields in the surrounding matter-free space. After deriving closed-form expressions for the vector spherical wave functions for the scattering material, the internal fields are represented as superpositions of those vector spherical wave functions. The unknown scattered-field coefficients are related to the known incident-field coefficients by a transition matrix. The total scattering and absorption efficiencies are highly affected by the orientation of the constitutive principal axes relative to the shape principal axes, and the effect of the orientational mismatch between the two sets of principal axes is more pronounced as the electrical size increases. The dependence of the total scattering efficiency, but not of the absorption efficiency, on the angle of rotation about a shape principal axis can be predicted qualitatively from the variation of a scalar function with respect to the angle of rotation. The total scattering and absorption efficiencies do not depend on the polarization state of incident plane wave when the scattering material is impedance-matched to free space. The polarization state of the incident plane wave has a more discernible effect on the total scattering and absorption efficiencies for ellipsoids compared to spheres.

Some objects feel colder to the touch than others at the same (room) temperature. But explaining why by linear, single-factor reasoning is inadequate because the time-dependent thermal energy transfer at solid interfaces initially at different temperatures is determined by the thermal inertia kρc, a function of three thermophysical properties: thermal conductivity k, density ρ, and specific heat capacity per unit mass c. In time-dependent problems 1/kρc plays the role of a resistance. As an example, although the thermal conductivity of aluminum is 16 times that of stainless steel, this does not translate into a 16-fold difference in interfacial thermal energy flux densities. Nor does it result in a markedly greater perceived coldness of aluminum; the difference is barely perceptible. Similarly, despite the 600-fold difference in the thermal conductivity of iron relative to that of wood, the ratio of thermal energy flux densities is only about 4.6.

In his interesting and informative book Is That a Fact?, Joe Schwarcz avers that pigs do not sweat and the saying “sweating like a pig” originates in iron smelting. Oblong pieces of hot iron, with a fancied resemblance to a sow with piglets, cool in sand to the dew point of the surrounding air, and hence water condenses on the “pig.” But this explanation, which I have seen on the Internet, lacks a few caveats. It implies that molten iron, solidifying and cooling, anywhere, anytime, accretes liquid water, as if this were a special property of cooling iron. Set aside that real pigs sweat perceptibly from their snouts; kiss a pig and verify for yourself. Pigs also sweat imperceptibly. Imperceptible (insensible) perspiration is water vapor from the skin and lungs exuded without sensible condensation. That from humans is about 1 liter/day. Sweat is 99% liquid water, NaCl the dominant solute, secreted quickly, sometimes profusely, by subcutaneous sweat glands in response to thermal stress, in contrast to the slow, continuous diffusion of water vapor through skin.

The simplest Lorentz-nonreciprocal medium has the constitutive relations (${\bf D} =\epso {\bf E} -{\bf \Gamma}\times {\bf H}$ and ${\bf B} =\muo {\bf H} + {\bf \Gamma}\times{\bf E}$). Scattering by a three-dimensional object composed of this medium was investigated using the extended boundary condition method. Scattering by this object in free space must be attributed to non-zero $\Gamma=\vert\bf \Gamma\vert$. The differential scattering efficiency is immune to the transformation of the incident toroidal electric field phasor into a poloidal electric field phasor, or \textit{vice versa}, and a consequence of this source-invariance is the polarization-state invariance of the differential scattering efficiency when the irradiating field is a plane wave. Both the total scattering and forward-scattering efficiencies of an ellipsoid composed of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is incident in a direction {coparallel (but not antiparallel)} to $\bf \Gamma$, and the backscattering efficiency is minimum when $\bf \Gamma$ is {parallel} to the incidence direction. The total scattering and the forward-scattering efficiencies are maximum when the incidence direction is parallel to the largest semi-axis of the ellipsoid if the incidence direction is coparallel (but not antiparallel) to $\bf \Gamma$. Lorentz nonreciprocity in an object is thus intimately connected to the shape of that object in affecting the scattered field., Comment: 22 pages, 8 figures

The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for co-moving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-co-moving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).

Effective-medium theories for electromagnetic constitutive parameters of particulate composite materials are theories of averages. Standard deviations are absent because of the lack of rigorous theories. But ensemble averages and standard deviations can be calculated from a rigorous theory of reflection by planar multilayers. Average reflectivities at all angles of incidence and two orthogonal polarization states for a multilayer composed of two kinds of electrically thin layers agree well with reflectivities for a single layer with the same overall thickness and a volume-weighted average of the relative permittivities of these two components. But the relative standard deviation can be appreciable depending on the angle of incidence and the polarization state of the incident illumination, and increases with increasing difference between the constitutive parameters of the two layers. This suggests that average constitutive parameters obtained from effective-medium theories do not have uniform validity for all calculations in which they might be used., 12 pages (accepted for publication in Journal of Modern Optics)

An Internet search for why objects, especially humans, cool more rapidly in water than in air, both at the same temperature, and by how much, yields off-the-cuff answers unsupported by experiment or analysis. To answer these questions in depth requires a smattering of engineering heat transfer, including radiative transfer, and the different thermophysical properties of the two fluids. The correct ratio for humans is closer to 2 than to 10, and if this were not so, swimming in cool water could be fatal.

To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce within illuminated objects. This can be shown directly by deriving the radiation force and torque resulting from normal-incidence illumination of a planar interface between free space and an arbitrary medium. Every point of the medium contributes to the total force and torque, which are therefore not localized.

The extended boundary condition method can be used to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident-field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The scattering, absorption, and extinction efficiencies were calculated thereby in relation to the propagation direction and the polarization state of the incident plane wave, the constitutive-anisotropy parameters, and the nonsphericity parameters of the ellipsoid, when the eigenvectors of the real permittivity dyadic are aligned along the three semi-axes of the ellipsoid. As the electrical size of the ellipsoid increases, multiple lobes appear in the scattering pattern. The total scattering efficiency can be smaller than the absorption efficiency for some configurations of the incident plane wave but not necessarily for others. The nonsphericity of the object has a stronger influence on the total scattering efficiency than on the absorption efficiency. The forward-scattering efficiency increases monotonically with the electrical size for all configurations of the incident plane wave, and so does the backscattering efficiency for some configurations. For other configurations, the backscattering efficiency has an undulating behavior with increase in electrical size and is highly affected by the shape and the constitutive anisotropy of the ellipsoid. Even though the ellipsoid is not necessarily a body of revolution, it is anisotropic, and it is not impedance matched to free space, the backscattering efficiency can be minuscule but the forward-scattering efficiency is not. This feature can be useful for harvesting electromagnetic energy.

Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather than to the general arguments about linearity, causality and analyticity in modern model-independent derivations. Kramers merely speculated on whether the specific results he obtained might have a more general validity. Neither author showed that a signal cannot travel faster than cin any medium for which the dispersion relations are satisfied. Indeed, they did not mention, even obliquely, signal speeds and causality. Despite their magical aura, Kramers–Kronig relations are translations into somewhat cryptic frequency language of statements clearer in time language.

Within the span of a year, I twice faced the same question in slightly different forms. The first time it came from Tom Schlatter, who fields questions from readers of Weatherwise. He wrote to me that a reader had “asked why running water freezes more slowly than still water. The stock answer is friction, but I would like to do better than that.” I responded with quantitative arguments that (fluid) friction is irrelevant, and there the matter stood.

Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics. It may—indeed sometimes should—precede or even supplant mathematical analysis. And yet dimensional analysis usually is given short shrift in physics textbooks, presented mostly as a diagnostic tool for finding errors in solutions rather than in finding solutions in the first place. Dimensional analysis is especially well suited to estimating the magnitude of errors associated with the inevitable simplifying assumptions in physics problems. For example, dimensional arguments quickly yield estimates for the errors in the simple expression 2h/g for the descent time of a body dropped from a height h on a spherical, rotating planet with an atmosphere as a consequence of ignoring the variation of the acceleration due to gravity g with height, rotation, relativity, and atmospheric drag.

In The Theory of Almost Everything,1 Robert Oerter asserts the following: “Take a beam of electrons that are all spinning in the same direction and fire it at, say, a brick. If you could keep this up for long enough, and if there were no other forces acting on the brick, the electrons would transfer their rotation to the brick, and it would begin to rotate.” Although this may awe credulous readers, skeptical physics students and their teachers ought to ask: Is it true that an electron can rotate a brick? To answer this requires bringing together elementary concepts from several areas of physics and doing the kind of back-of-the-envelope calculations students should be taught to do early on in their scientific education.

The Figuring Physics that appeared in our April 2007 issue has drawn a number of responses. The question posed by Paul Hewitt in that piece had to do with evaporative cooling: “Consider four grams of boiling water poured onto a cold surface. Suppose one gram rapidly evaporates by absorbing 540 calories from the remaining three grams of water, ideally with no other heat transfer occurring. The remaining three grams will become (a) water at a temperature above 0°C, (b) water at 0°C, or (c) ice at 0°C.” Hewitt's answer (c) drew protests from readers who argued that this would violate the second law of thermodynamics.

Green thunderstorms have been observed from time to time in association with deep convection or severe weather events. Often the green coloration has been attributed to hail or to reflections of light from green foliage on the ground. Some skeptics who have not personally observed a green thunderstorm do not believe that green thunderstorms exist. They suggest that the green storms may be fabrications by excited observers. The authors have demonstrated the existence of green thunderstorms objectively using a spectrophotometer. During the spring and summer of 1995 the authors observed numerous storms and recorded hundreds of spectra of the light emanating corn these storms. It was found that the subjective judgment of colors can vary somewhat between observers, but the variation is usually in the shade of green. The authors recorded spectra of green and nongreen thunderstorms and recorded spectral measurements as a storm changed its appearance from dark blue to a bluish green. The change in color ...

Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere's comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal's spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere's velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere's velocity, when the sphere's speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere's velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal's direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation. >

The severest test of a theory of scattering by particles is how well it calculates scattering in the backward direction. The coupled-dipole method can be used for accurately calculating backscattering at 94 GHz by hexagonal ice crystals. Backscattering by columns is markedly different from that by plates, which indicates that it might be possible to infer size and shape distributions of ice crystals using recently developed millimeter wave radar.

Near-forward scattering by cloud droplets is known to give rise to colored rings, centered on the Sun or the Moon, which are called the corona. Because of the spherical shape of the droplets, the corona can be circular. A Finnish amateur astronomers' network has found a corona, in a seemingly cloudless sky, with a regular vertically elliptical shape. The aspect ratio of these ellipses changes with the altitude of the Sun or the Moon. Some brightening in the coronas has also been reported. Because of observations of high pollen concentrations at the time of occurrence of these coronas, we propose that some coronas can be explained as a result of scattering by birch pollen grains, which are more or less spheroidal. To explain other observed coronas, pollen grains with more complicated shapes, such as pine and spruce pollen grains, must be invoked. Our analysis is limited to spheroidal grains, for which the Fraunhofer theory gives analytical expressions of simple form. The more complicated shapes require numerical simulations or laboratory experiments, which we have not done.

If the Sun can be seen at all through thin clouds it usually has a sharp edge, although occasionally it appears fuzzy, especially through altostratus, but rarely, if ever, through fog. Experiments with suspensions of polystyrene spheres of different sizes and optical thicknesses suggest that the range of cloud optical thicknesses over which a fuzzy Sun is seen increases with particle size. Nonsphericity, turbulence, and cloud horizontal inhomogeneity are not necessary for fuzziness. A possible explanation for what is observed is that, for a given optical thickness, the modulation contrast function of a cloud decreases more rapidly with increasing frequency the greater the particle size. Consequently the transition from optical thicknesses for which contrast is above the contrast threshold at all spatial frequencies to optical thicknesses for which contrast is below the threshold at high frequencies is sufficiently gradual to permit fuzziness of the Sun to be observed through clouds of constantly changing opt cal thickness.

Suspensions of wire helices are absorbing at microwave frequencies. Although such suspensions are chiral, this may be accidental rather than essential for absorption in coatings. Nonchiral suspensions of connected loop arrays behave similarly to suspensions of helices.

This issue of Applied Optics features 36 papers on topics related to particle sizing by optical methods. The contributions to this special issue derive primarily, though not exclusively, from papers presented at the Second International Congress on Optical Particle Sizing held in Tempe, Arizona, on 5–9 March 1990. The congress was the second in what we hope will be a continuing series of international meetings, held at 3-year intervals, on topics related to particle-size measurements by optical techniques. The 1990 Congress built on the successful First International Congress held in Rouen, France, in 1987. A third Congress is planned for 1993 in Yokohama, Japan.

Colors in birefringent airplane windows seen through polarizing filters are not especially pure nor are all colors equally probable. This is a consequence of the shape of transmission vs wavelength for a retarder–polarizer combination illuminated by partially polarized skylight. Although transmission can have a single peak in the blue or green, a peak in the red is accompanied by one in the blue. This and the general blueness of skylight are why the purest colors seen in airplane windows are greens, yellowish-greens, and purples (mixtures of red and blue). Purer colors and a wider gamut are obtained for birefringent sheets interposed between dichroic polarizing filters and illuminated by tungsten light.

When this work was done the author was with Los Alamos National Laboratory, Life Sciences Division, Los Alamos, New Mexico 87545; he has now returned to Pennsylvania State University, Meteorology Department, University Park, Pennsylvania 16802.

An optical model for the pelt of a polar bear is presented that accounts for ultraviolet light and other optical properties that the bear's pelt has been known to exhibit. (AIP)

Fall streaks are arcs in the sky composed of ice crystals falling from high‐altitude cirrus clouds. With the crystals falling at their vertical terminal velocity and their horizontal velocity that of the local wind, the streaks are parabolas if the wind increases linearly with height. The dynamics of fall streaks is formally identical with that of drag‐free projectiles−but with a twist: the roles of horizontal and vertical coordinates are reversed.

The visual phenomenon called virga, a sudden change in the brightness of a precipitation shaft below a cloud, is commonly attributed to evaporation of raindrops. It is said to be rain that does not reach the ground. The optical thickness of an evaporating rain shaft, however, decreases gradually from cloud base to ground. Thus, it is more likely that virga results from snowflakes melting in descent. Horizontal optical-thickness decreases of more than ten can occur in the short distance over which a snowflake is transformed into a raindrop. This decrease is caused by two factors: a smaller number density of hydrometeors because of the greater fall velocity of raindrops than of equivolume snowflakes, and a smaller scattering cross section: the first of these is dominant. An alternative explanation of virga is that it is precipitation that has not yet reached (rather than does not reach) the ground. This is a plausible explanation given the long time periods it may take hydrometeors, especially snow...

Isotropic chiral materials are rotationally symmetric but not mirror symmetric. Their salient optical property is that only a circularly polarized plane wave can propagate (in any direction) in them without change in polarization. In general, the major axis of an elliptically polarized plane wave changes direction—called optical rotation—and its ratio of minor to major axes increases. Such materials have different wavenumbers for circularly polarized waves of opposite handedness. The equations for arbitrary time-harmonic electromagnetic fields can be cast in a form such that every problem that has ever been solved for linear, isotropic achiral materials (such as reflection and transmission by layers, and scattering by particles) can also be solved for linear, isotropic chiral materials.

The coupled dipole model of scattering by an arbitrary particle has been reformulated in terms of internal scattering processes of all orders. This formalism readily permits physical interpretation of observables and provides a rational basis for making computations more efficient. The calculation of scattering parameters can be simplified by appropriately terminating the infinite series at any order as well as by restricting the summations over the dipolar interaction terms within each order. Large particles can be partitioned into segments so that the scattered field is a superposition of the fields from the segments together with fields due to interactions among dipoles in different segments.