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Can a flame cast a shadow? The blocker theory of shadows answers no because flames emit light. However, a candle on a white surface does appear to cast a flame. Denying that the dark patch created by the flame is a shadow saves the blocker theory of shadows. It is instead a shadowgram – a kind of para-refraction much like the para-reflections of the preceding chapters.

This chapter studies wave interference. Light does not bend in a lens, it does not bounce off the surface of glass, and it does not spread out after passing through a small hole. All of these are illusions. It only appears that light bends, bounces, and spreads out. The effects that people see—reflection, refraction, colors in soap bubbles—come from the fact that photons interact with one another in an unusual way. The interaction is often referred to as wave interference because it can be described mathematically much like the interference of water waves, but the reality of it is considerably stranger. The strangeness is discussed in more detail in the last chapter, but a hint of it can be seen from the fact that photons appear to interfere with one another even if they are emitted one at a time, which water waves obviously do not do.

Refraction and small-angle scattering can provide unique imaging signals in situations where absorption- or other attenuation-based effects are insufficient. Attenuation contrast is low in cases where either the absolute values of the attenuation coefficients of the individual components of the object are low, or the differences between the various components are small. In such cases, other contrast mechanisms have to be employed for imaging such as the phase contrast described in the previous chapter. This chapter discusses two additional contrast mechanisms: refraction tomography and small-angle scattering tomography. Experimental results for both techniques are presented.

The basic assumption of ‘rational mechanics’ was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, the rest of natural philosophy would fall into place around it. The guiding idea, from Varignon and Hermann at the beginning of the eighteenth century, up to d'Alembert and Euler in mid‐century, was that mechanics could be pursued independently of other natural‐philosophical considerations, that it was the one absolutely secure physical discipline because of its mathematical (and effectively a priori) standing. The chapter explores the rational mechanics of d'Alembert and Euler, and questions whether what was proposed in fact had an a priori standing, and whether it was plausible to assume that recalcitrant phenomena such as the refraction of light, the behaviour of fluids, and gravitation could be accounted for by mechanics.

This chapter discusses electrical phenomena in space and molecules. Topics covered include molecular dipoles, absorption and emission by molecules, Raman effect, electronic transitions in molecules, Morse curves, the Franck-Codon principle, the electromagnetic theory of light, refraction and dispersion, optical activity, and a selection rules for transitions between states.

This chapter shows that Newton developed a theory of refraction based on the chymical principle sulfur, which he described in the first edition Opticks (1704). It also finds that the seeds of this theory extend back to Newton's 1675 Hypothesis of Light, where he explicitly abandons the Sendivogian theory of an aerial niter that he had affirmed in Of Natures obvious laws. Newton replaced the aerial niter, which had accounted for phenomena ranging from combustion and respiration to the fertilization of the earth, with a growing reliance on sulfur. Although he had reasons of his own for making this shift, Newton was also influenced by parallel developments in European chymistry, a field that was rapidly moving toward what would eventually be known as phlogiston theory.

Reveals the beginnings of several important projects during Descartes's time in the army of Maximilian I, stationed at Ulm. These include the composition of the first part of the Regulae ad directionem ingenii, a general theory of method, which provoked a series of dreams, a doctrine of analysis, a work on solid geometry and figurate numbers and, possibly, the discovery of the sine law of refraction. Discusses the relationship between deduction and intuition, Descartes's doctrine of cognition and that of the Stoics, and Descartes's doctrine of clarity and distinctness in comparison with Aristotle's and Quintillian's doctrine of vividness and particularity.

Describes Descartes's time in Paris and the intellectual milieu in which he moved. Reconstructions by Schuster and Shea of his discovery, whilst collaborating with Mydorge on optics, of the law of refraction. Detailed account of the latter part of the Regulae, in which he dealt with cognition and mechanism in the form of a general natural philosophy, the problem of mortalism, and his preference for algebra over geometry in problem‐solving. His search for certainty is ascribed to his interest in the relationship between mechanism, and clarity, and distinctness, rather than an interest in scepticism.

This chapter gives a theoretical description of the basic properties of electromagnetic radiation. Maxwell's equations are first reviewed; the expressions of electrodynamic potentials in the vacuum and in polarized media are then given. The classic theory of the scattering of X-rays by electrons is described (Thomson scattering). The dielectric susceptibility (polarizability) of matter for X-rays and the Fourier expansions of its real and imaginary parts in a periodic medium (index of refraction, atomic scattering factor, and absorption coefficient) are discussed. A detailed account of Ewald's dispersion theory that is at the base of Ewald's dynamical theory is then presented. The propagation equation of X-rays, which is used throughout the book, is derived from Maxwell's equations according to Laue's basic assumptions. The last part of the chapter is devoted to specular reflection and Fresnel relations.

This chapter is the first of the next few chapters devoted to plane-wave advanced dynamical theory. The fundamental equations of dynamical diffraction are derived for vector waves and the expression of the dispersion equation is given in the two-beam case and for absorbing crystals, the following discussion being limited to geometrical situations where neither the incidence nor the emergence angle is grazing. The notion of wavefields and the dispersion surface are introduced, and it is shown that the Poynting vector, which gives the direction of propagation of the energy, is normal to it. The boundary conditions at the entrance surface are then introduced. Transmission and reflection geometries are treated separately. For each case, the deviation parameter is introduced geometrically and the coordinates of the tiepoints determined, the Pendellösung distance (extinction distance in the reflection geometry), Darwin width, the anomalous absorption coefficient, index of refraction, the phase and amplitude ratios of the reflected and refracted waves are calculated. Borrmann's standing wave interpretation of the anomalous absorption effect is given. The last section is to the case where Bragg's angle is close to π/2.

This chapter describes the propagation of wavefields inside the crystal close to the Bragg angle. It shows that the direction of propagation of packets of wavefields as obtained by their group velocity is identical to that of the Poynting vector. The geometrical properties of wavefields trajectories (ray tracing) within the Borrmann triangle are determined and the intensity distribution along the base of the Borrmann triangle is calculated. A detailed account of the experimental observation of the double refraction of the X-ray wavefields at the Bragg angle is given. The propagation of wavefields in finite crystals giving rise to partial reflections and interference effects is then described. The Bragg–Laue, Bragg–Bragg, and Laue–Bragg geometries are successively considered, and the formation of the Borrmann–Lehmann fringes in the latter case analyzed. In the last section, the coherence properties of X-ray sources are discussed.

This chapter develops the theory of band-to-band and band impurity transitions involving photon absorption. Topics discussed include basic theory of absorption and gain, direct interband absorption, indirect transitions, intersubband absorption, band impurity absorption, effect of heavy doping and carrier injection, and carrier-induced change in absorption and refraction. Exercises are provided at the end of the chapter.

This chapter explains occurrences during and after the Scientific Revolution, in which the personification of nature that is at the heart of the Aristotelian philosophy had a nasty way of reappearing in the most orthodox of machine-metaphor- influenced places. Even more than mechanics, optics was riddled with final-cause thinking. Pierrre de Fermat's “principle of least time” explains Snell's law of refraction, the connection between the angle of incidence and the angle of refraction. Since light going from a less dense to a denser medium is bent toward the normal, it is not going from beginning to end by the shortest distance. But assuming that light travels less quickly in a more dense than less dense medium, one can show that it does travel in the shortest time.

The horizon enlargement of the celestial bodies cannot be explained by variations in their real distance, a fact recognised by astronomers since at least the time of Hipparchus in the second century BC. Many scientists nevertheless thought the enlargement was real, and they have attributed this solely to an enlarging effect of the Earth’s atmosphere. This idea developed from Aristotle’s rudimentary ideas on atmospheric vapours in the fourth century BC to a fairly explicit theory some 500 years later, and then gradually degenerated to its more primitive form over many centuries. Yet so compelling is the moon illusion that even in modern times many people regard the enlargement as real, and attribute it to some atmospheric effect. This chapter looks at atmospheric refraction, initially believed to be the cause of the moon illusion. Optical magnification through water and telescopes does not produce the degree of perceptual enlargement predicted by optical theory.

The main purpose of this chapter is to show how Ptolemy combined all three approaches discussed in the previous chapter in order to create a theory of sight that accounts broadly not only for visual perception per se but also for visual misperception: i.e., visual illusions, which Ptolemy attributed to improper physical conditions, interference with the normal functioning of the visual system, or psychological deception. Two types of illusion—image-displacement and deformation according to reflection and refraction—were of paramount concern to Ptolemy, whose analysis of reflection and refraction in books 3-5 of the Optics remained more or less canonical until the seventeenth century. In fact, as claimed at the end of the chapter, Ptolemy set the agenda for optics as it developed until the early modern period, much as his Almagest set the agenda for astronomy.

Conceptually, the basic optical methods used to perform an ‘objective’ refraction are simple. However, these elementary optical procedures are not always simple to implement and are invariably affected by the conditions under which they are used. This chapter is written to help the professional who works with infants but who does not perform eye examinations, to understand the procedures and problems encountered while refracting an infant. The discussion of the six conditions, under which refractions can be performed and which affect the results of the refraction, involves a more complex analysis than the basic refractive procedure. The most widely used objective refracting device is the retinoscope. It is objective only in the sense that the patient's subjective impressions are not used. However, the retinoscopist must make a complex series of subjective decisions. How the retinoscope works is explained in this chapter. The less widely used autorefractors use variations on the same optical principles employed by the retinoscope.

In the middle ages (550-1510 CE) scientific knowledge was consolidated and translated, first from Greek and Latin into Arabic and Syriac and then from Arabic and Greek into Latin. Alhazen (1020 CE) was an important Arabic speaking scholar who made important contributions to a theory of vision and of refraction. Oresme and the school of Oxford scholars were the first (1360 CE) to describe uniform acceleration graphically. Leonardo De Vinci was a prolific inventor and user of informative diagrams – one of which describes the cause of “earthshine” (1520 CE).

The early modern period (1543-1785) contributed many physical concepts that are simple enough to be conveyed with a diagram. Copernicus’s heliocentric universe (1543), Galileo’s discovery of the mountains on the moon (1610), Kepler’s laws of planetary motion (1620), Boyle’s law (1662), Newton’s theory of color (1666), and Bernoulli’s principle (1733) are but six of the eighteen topics covered in this period. Experiments and observations that generated measurements became the norm.

The purpose of this chapter and the following one is to explore and explain the rich diversity of Stokes’s contributions to physical optics in Cambridge and world contexts. He triggered debates and inspired friends through his semi-private speculations on the nature and motion of the ether in stellar aberration, double refraction, and optical rotation. He discussed deep-seated analogies between hydrodynamics and optics. He consolidated the fundamental laws of wave optics through mathematically sophisticated theories of interference, including Newton’s rings; diffraction, for which he provided a dynamical theory; and polarization. His theoretical achievements were backed up by carefully designed and extremely precise experiments.