## References and Suggestions for Further Reading

For a biography of Maxwell see Ivan Tolstoy, 1981 James Clerk Maxwell A Biography. University of Chicago. This is a model of scientific biography comprehensible to a non-scientific audience. It is short, well written, and without a single equation conveys the contributions of a scientist whose fame rests mostly on equations. For a much more detailed and technical history of electromagnetism (including electromagnetic radiation) see Edmund Whittaker, 1987 A History of the Theories of Aether and...

## Radiance

Before tackling radiance we need one more result. Consider a monodirectional, monochromatic, uniform beam of light. To obtain a measure of the amount of radiant energy transported by the beam we imagine a surface A to be placed in the beam with the normal to the surface parallel to it (Fig. 4.2). We can in principle determine how many photons in unit time No cross A No multiplied by the photon energy is the amount of radiant power (energy per unit time) crossing A. Divide this quantity by A to...

## Radiation in Equilibrium with Matter

We often are told that when bodies are heated they radiate or that hot bodies radiate. True enough, but it is just as true that when bodies are cooled they radiate and that cold bodies radiate. All matter - gaseous, liquid, or solid - at all temperatures emits radiation of all frequencies at all times, although in varying amounts, possibly so small at some frequencies, for some materials, and at some temperatures as to be undetectable with today's instruments (tomorrow's, who knows ). Note that...

## Brightness and Color Temperature

Suppose we have an instrument that can measure radiant power over some range of frequencies anywhere in the electromagnetic spectrum. For simplicity we assume a narrow field of view for the instrument, but this is not necessary. If we were to point the instrument in a particular direction at a source of radiation, which could, but need not, be a measurably emitting body, the instrument would dutifully measure a radiant power. Now we can ask, What temperature must a blackbody have in order for...

## Acoustic Waves

We noted that Eq. (3.52) is the governing equation for acoustic waves. Waves on a string can be looked upon as one-dimensional acoustic waves in that they are governed by this equation in one dimension. And waves on the strings of musical instruments excite three-dimensional acoustic waves in the air surrounding them. Although our primary interest is (vector) electromagnetic waves, acoustic waves in fluids are scalar waves and hence simpler. For this reason we often draw analogies between...

## Distinction between a Theory and an Equation

We criticized the simple theory of the two-slit interference pattern which is based on the physically incorrect assumption that empty space (slits) is a source of waves. Why, then, does this theory give correct results (sometimes) Consider first an opaque screen with no slits and illuminated on one side. No light is transmitted. Why If you accept the superposition principle for electromagnetic waves, you cannot believe that the incident wave is destroyed. It exists everywhere just as it did...

## Molecules and Particles Similarities and Differences

As far as absorption (or scattering) is concerned a molecule is a particle of zero dimensions. Although molecules do indeed have extension in space they are fuzzy. In any interaction of electromagnetic radiation with matter, the relevant measuring stick is the wavelength, against which molecules are quite small, even for wavelengths well into the ultraviolet. The separate parts of molecules therefore radiate in unison. A corollary of this is that absorption by molecules and by small (compared...

## Polarization The Hidden Variable

We call polarization the hidden variable because it is a property of light not readily observed with the unaided eye. Everyone is aware of variations in color and brightness, so in teaching about these properties of light we can appeal to observations that everyone has made or can make with little effort. Alas, this is not so with the polarization of light, which to observe requires a bit of effort and, more important, a few simple tools. Once you have fully grasped polarized light, however,...

## Scattering An Overview

Why is light scattered No single answer will satisfy everyone, yet because scattering by particles is amenable to treatment mostly by classical electromagnetic theory, our answer lies within this theory. Although palpable matter may appear continuous and often is electrically neutral, it is composed of discrete electric charges. Light is an oscillating electromagnetic field, which can excite these charges to oscillate. Oscillating charges radiate electromagnetic waves, a fundamental property of...

## Problems

To gain confidence that the N-stream equation Eq. (6.2) is correct (within the limits of the underlying approximations), show that it is correct for four streams. For simplicity take two directions in the downward hemisphere, two in the upward hemisphere, and the cosines in the downward direction equal in magnitude but opposite in sign to those in the upward hemisphere. Don't forget that attenuation is along a direction of propagation, which corresponds to the 2 direction only for light...

## The Nature of Polarized Light

The more times you see an explanation of a physical phenomenon or a statement about physical reality, especially in the form of an invariable mantra, especially in a textbook unaccompanied by any qualifications, the more certain you can be that it is wrong. Stated more succinctly, repetition increases the probability of incorrectness. This is a law of almost universal validity. One example is the assertion that the electric and magnetic fields of light waves are always perpendicular to each...

## Path Length Distribution

The probability distribution for the path length x a photon travels before it is scattered or absorbed is given in Section 5.1, rewritten here as where x is the physical path length and t the total mean free path. It is more convenient here to express this distribution in terms of the optical path length r x t the integral of which from 0 to to is 1, as it must be if this is a proper probability distribution. As we did previously for the probability distribution 2x, we find r as a function of ,...

## Pdysaid d dy

Figure 6.4 The continuous probability distribution p exp(-t) for the variable t can be approximated by dividing the t-axis into equal intervals (bins) 1000 bins were used here. Values are assigned to each bin with a random number generator. The number of values in each bin divided by the total number times the bin width is the probability density for the bin. The discrete probability densities (solid circles) more closely approximate the continuous distribution (solid line) the greater the...

## Absorption Cross Section

Determining the absorption coefficient of liquids and solids from the absorption properties of their individual molecules is not an easy task because they are sufficiently close together that they interact strongly. This is evident from Figs. 1.11 and 1.12, which show that the spectral emissivity of liquid water bears little resemblance to that of water vapor. Beginning with the latter it is not an easy step to the former. Interactions between water molecules in the liquid phase all but destroy...

## The General Radiation Field

Light is a superposition of electromagnetic waves, intertwined electric fields E and magnetic fields H. Because these fields are vectors, so are electromagnetic waves. They satisfy vector wave equations similar to the scalar wave equation derived in Section 3.3 for the vibrating string. We usually are most interested in the rate at which radiant energy is transported by electromagnetic waves. The electric and magnetic fields determine this transport rate by way of the Poynting vector where E...

## Wave and Particle Languages

We may discuss electromagnetic radiation using two languages wave or particle (photon) language. As with all languages, we sometimes can express ideas more succinctly or clearly in the one language than in the other. We use both, separately and sometimes together in the same breath. We need fluency in both. Much ado has been made over this supposedly lamentable duality of electromagnetic radiation. But no law requires physical reality to be described by a single language. We may hope for such a...

## Classical versus Quantum Mechanical Interpretation of Absorption

What once was, and perhaps still is, the standard treatise on atomic spectra, by Condon and Shortley, fills 432 pages of text. Herzberg's treatises fill 581 pages for diatomic molecules, 538 pages for polyatomic molecules, and 670 pages for the electronic spectra of polyatomic molecules. Townes and Schawlow devote 648 pages to microwave spectroscopy. And the physical strain of just lifting these nearly 3000 pages is as nothing compared to the mental strain of absorbing them. Add to these tomes...

## Scattering by an Isotropic Homogeneous Sphere

An isotropic, homogeneous sphere is the simplest finite scatterer, the theory of scattering by which is attached to the name of Gustav Mie. So firm is this attachment that in defiance of logic and history every particle under the sun has been dubbed a Mie scatterer, and Mie scattering has been promoted from a particular theory of limited applicability to the unearned rank of general scattering process. Mie was not the first to solve the problem of scattering by an arbitrary sphere. It would be...