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The Greek term ?? ?????? referred specifically to matters of vision^[1], and hence early optics was concerned with the problem of how we see. The early writers discussed here treated vision more as a geometrical than as a physical, physiological, or psychological problem.

The first known author of a treatise on optics was the geometer Euclid (c. 325 BC?265 BC). Euclid began his study of optics as he began his study of geometry, with a set of self-evident axioms.

Euclid did not define the physical nature of these visual rays but, using the principles of geometry, he discussed the effects of perspective and the rounding of things seen at a distance.

Where Euclid had limited his analysis to simple direct vision, Hero of Alexandria (c. AD 10-70 ) extended the principles of geometrical optics to consider problems of reflection (catoptrics). Unlike Euclid, Hero occasionally commented on the physical nature of visual rays, indicating that they proceeded at great speed from the eye to the object seen and were reflected from smooth surfaces but could become trapped in the porosities of unpolished surfaces.^[2]

Hero demonstrated the equality of the angle of incidence and reflection on the grounds that this is the shortest path from the object to the observer. On this basis, he was able to define the fixed relation between an object and its image in a plane mirror. Specifically, the image appears to be as far behind the mirror as the object really is in front of the mirror.

Like Hero, Ptolemy (c. 90 ? c. 168) considered the visual rays as proceeding from the eye to the object seen, but, unlike Hero, considered that the visual rays were not discrete lines, but formed a continuous cone. Ptolemy extended the study of vision beyond direct and reflected vision; he also studied vision by refracted rays (dioptrics), when we see objects through the interface between two media of different density. He conducted experiments to measure the path of vision when we look from air to water, from air to glass, and from water to glass and tabulated the relationship between the incident and refracted rays.^[3]

His tabulated results have been studied for the air water interface, and in general the values he obtained reflect the theoretical refraction given by modern theory, but the outliers are clearly distorted to represent Ptolemy's a priori model of the nature of refraction.

Al-Kindi (c. 801?873) was one of the earliest important optical writers in the Islamic world. In a work known in the west as De radiis stellarum, al-Kindi developed a theory "that everything in the world ... emits rays in every direction, which fill the whole world."^[4] It is believed that this theory of the active power of rays influenced such Western scholars as Robert Grosseteste and Roger Bacon^{[citation needed]}.

Ibn Sahl (c. 940-1000) was a mathematician associated with the court of Baghdad. About 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light. In his work he discovered a law of refraction mathematically equivalent to Snell's law.^[5] He used his law of refraction to compute the shapes of lenses and mirrors that focus light at a single point on the axis.

Ibn al-Haytham (known in Western Europe as Alhacen) (965-1040), often regarded as the "father of optics",^[6] formulated "the first comprehensive and systematic alternative to Greek optical theories."^[7] His key achievement was twofold: first, to insist that vision only occurred because of rays entering the eye and that rays postulated to proceed from the eye had nothing to do with it; the second was to define the physical nature of the rays discussed by earlier geometrical optical writers, considering them as the forms of light and color. He developed a camera obscura to demonstrate that light and color from different candles passed through a single aperture in straight lines, without intermingling at the aperture.^[8] He then analyzed these physical rays according to the principles of geometrical optics. Ibn al-Haytham also employed the experimental scientific method as a form of demonstration in optics. He wrote many books on optics, most significantly the Book of Optics (Kitab al Manazir in Arabic), translated into Latin as the De aspectibus or Perspectiva, which disseminated his ideas to Western Europe and had great influence on the later developments of optics.^[9]

The English bishop, Robert Grosseteste (c. 1175 - 1253), wrote on a wide range of scientific topics at the time of the origin of the medieval university and the recovery of the works of Aristotle. Grosseteste reflected a period of transition between the Platonism of early medieval learning and the new Aristotelianism, hence he tended to apply mathematics and the Platonic metaphor of light in many of his writings. He has been credited with discussing light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, and a theology of light.^[10]

Setting aside the issues of epistemology and theology, Grosseteste's cosmogony of light describes the origin of the universe in what may loosely be described as a medieval "big bang" theory. Both his biblical commentary, the Hexaemeron (1230 x 35), and his scientific On Light (1235 x 40), took their inspiration from Genesis 1:3, "God said, let there be light", and described the subsequent process of creation as a natural physical process arising from the generative power of an expanding (and contracting) sphere of light.^[11]

His more general consideration of light as a primary agent of physical causation appears in his On Lines, Angles, and Figures where he asserts that "a natural agent propagates its power from itself to the recipient" and in On the Nature of Places where he notes that "every natural action is varied in strength and weakness through variation of lines, angles and figures."^[12]

The English Franciscan, Roger Bacon (c. 1214 ? 1294) was strongly influenced by Grosseteste's writings on the importance of light. In his optical writings (the Perspectiva, the De multiplicatione specierum, and the De speculis comburentibus) he cited a wide range of recently translated optical and philosophical works, including those of Alhacen, Aristotle, Avicenna, Averroes, Euclid, al-Kindi, Ptolemy, Tideus, and Constantine the African. Although he was not a slavish imitator, he drew his mathematical analysis of light and vision from the writings of the Arabic writer, Alhacen. But he added to this the Neoplatonic concept, perhaps drawn from Grosseteste, that every object radiates a power (species) by which it acts upon nearby objects suited to receive those species.^[13] Note that Bacon's optical use of the term "species" differs significantly from the genus / species categories found in Aristotelian philosophy.

Another English Franciscan, John Pecham (died 1292) built on the work of Bacon, Grosseteste, and a diverse range of earlier writers to produce what became the most widely used textbook on Optics of the Middle Ages, the Perspectiva communis. His book centered on the question of vision, on how we see, rather than on the nature of light and color. Pecham followed the model set forth by Alhacen, but interpreted Alhacen's ideas in the manner of Roger Bacon.^[14]

Like his predecessors, Witelo (c. 1230 - 1280 x 1314) drew on the extensive body of optical works recently translated from Greek and Arabic to produce a massive presentation of the subject entitled the Perspectiva. His theory of vision follows Alhacen and he does not consider Bacon's concept of species, although passages in his work demonstrate that he was influenced by Bacon's ideas. Judging from the number of surviving manuscripts, his work was not as influential as those of Pecham and Bacon, yet his importance, and that of Pecham, grew with the invention of printing.^[15]

Before quantum optics became important, optics consisted mainly of the application of classical electromagnetism and its high frequency approximations to light. Classical optics divides into two main branches: geometric optics and physical optics.

Geometric optics, or ray optics, describes light propagation in terms of "rays". Rays are bent at the interface between two dissimilar media, and may be curved in a medium in which the refractive index is a function of position. The "ray" in geometric optics is an abstract object which is perpendicular to the wavefronts of the actual optical waves. Geometric optics provides rules for propagating these rays through an optical system, which indicates how the actual wavefront will propagate. Note that this is a significant simplification of optics, and fails to account for many important optical effects such as diffraction and polarization.

Geometric optics is often simplified even further by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial raytracing, which are used to find first-order properties of optical systems, such as approximate image and object positions and magnifications. Gaussian beam propagation is an expansion of paraxial optics that provides a more accurate model of coherent radiation like laser beams. While still using the paraxial approximation, this technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.

Physical optics or wave optics builds on Huygen's principle and models the propagation of complex wavefronts through optical systems, including both the amplitude and the phase of the wave. This technique, which is usually applied numerically on a computer, can account for diffraction, interference, and polarization effects, as well as aberrations and other complex effects. Approximations are still generally used, however, so this is not a full electromagnetic wave theory model of the propagation of light. Such a full model would (at present) be too computationally demanding to be useful for most problems, although some small-scale problems can be analyzed using complete wave models.

Optics  is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. Optics explains optical phenomena.

The field of optics usually describes the behavior of visible, infrared, and ultraviolet light; however because light is an electromagnetic wave, analogous phenomena occur in X-rays, microwaves, radio waves, and other forms of electromagnetic radiation. Optics can thus be regarded as a sub-field of electromagnetism. Some optical phenomena depend on the quantum nature of light relating some areas of optics to quantum mechanics. In practice, the vast majority of optical phenomena can be accounted for using the electromagnetic description of light, as described by Maxwell's Equations.

Optics, as a field, is often considered largely separate from the physics community. It has its own identity, societies, and conferences. The pure science aspects of the field are often called optical science or optical physics. Applied optical sciences are often called optical engineering. Applications of optical engineering related specifically to illumination systems are called illumination engineering. Each of these disciplines tends to be quite different in its applications, technical skills, focus, and professional affiliations. More recent innovations in optical engineering are often categorized as photonics or optoelectronics. The boundaries between these fields and "optics" are often unclear, and the terms are used differently in different parts of the world and in different areas of industry.

Because of the wide application of the science of "light" to real-world applications, the areas of optical science and optical engineering tend to be very cross-disciplinary. Optical science is a part of many related disciplines including electrical engineering, physics, psychology, medicine (particularly ophthalmology and optometry), and others. Additionally, the most complete description of optical behavior, as known to physics, is unnecessarily complicated for most problems, so particular simplified models are used. These limited models adequately describe subsets of optical phenomena while ignoring behavior irrelevant and/or undetectable to the system of interest

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