Treatise on Light: In Which Are Explained the Causes of That Which Occurs in Reflection & Refraction (French: Traité de la Lumière: Où sont expliquées les causes de ce qui luy arrive dans la reflexion & dans la refraction) is a book written by Dutch polymath Christiaan Huygens that was published in French in 1690. The book describes Huygens's conception of the nature of light propagation which makes it possible to explain the laws of geometrical optics shown in Descartes's La Dioptrique, which Huygens aimed to replace. Unlike Newton's corpuscular theory, which was presented in the Opticks, Huygens conceived of light as an irregular series of shock waves which proceeds with very great, but finite, velocity through the ether, similar to sound waves. Moreover, he proposed that each point of a wavefront is itself the origin of a secondary spherical wave, a principle known today as the Huygens–Fresnel principle. The book is considered a pioneering work of theoretical and mathematical physics and the first mechanistic account of an unobservable physical phenomenon.
Overview Huygens worked on the mathematics of light rays and the properties of refraction in his work Dioptrica, which began in 1652 but remained unpublished, and which predated his lens grinding work. In 1672, the problem of the strange refraction of the Iceland crystal created a puzzle regarding the physics of refraction that Huygens wanted to solve. Huygens eventually was able to solve this problem by means of elliptical waves in 1677 and confirmed his theory by experiments mostly after critical reactions in 1679. His explanation of birefringence was based on three hypotheses: (1) there are inside the crystal two media in which light waves proceed, (2) one medium behaves as ordinary ether and carries the normally refracted ray, and (3) the velocity of the waves in the other medium is dependent on direction, so that the waves do not expand in spherical form, but rather as ellipsoids of revolution; this second extraordinary medium carries the abnormally refracted ray. By studying the symmetry of the crystal, Huygens was able to determine the direction of the axis of the ellipsoids, and from the refraction properties of the abnormal ray he established the proportion between the axes. He calculated the refraction of rays on plane sections of the crystal other than the natural crystal sides, and ultimately verified many of his results experimentally. Huygens intended to publish his results as part of the Dioptrica but decided to separate his theory of light from the rest of the work at the last minute, marking the transition from geometrical to physical optics. More than a century later, it would take Étienne Malus and others fifteen years to reconstruct Huygens's ideas of rays and wavefronts.
Contents
Propagation medium In the first chapter, Huygens describes light as a disturbance which moves in a material medium of an unknown nature which he calls ethereal, and which is different from that which propagates sound. This ethereal matter is composed of elastic particles of matter which collide according to laws he discovered in 1669. Huygens considers that the structure of matter is atomic, made up of an assembly of particles "which touch each other without composing a continuous solid." Light waves can therefore move from one particle to another without these being displaced. Another way of looking at the problem of propagation is to consider that it is not the particles of the transparent medium which transmit light but the particles of ethereal matter which permeate the interstices of the solid or liquid matter (or even a vacuum, since light passes through the top of Torricelli's barometer). Finally, Huygens considers a third type of light propagation that would be a combination of the first two. Another concept discussed in the first chapter is the speed of light, where Huygens originally takes up the temporal conception of Pierre de Fermat. He considers that the "shaking" producing light waves necessarily moves at finite speed, even if it is very high. This point is very important because its demonstrations are based on the equivalence of travel times on different paths. Huygens reports on a letter by Ole Christensen Rømer, dated from 1677, where the speed of light is said to be at least 100,000 times faster than the speed of sound, and possibly six times higher. In the latter case, the speed found by Rømer (214,000 km /s) was of the same order of magnitude as the speed of light admitted today.
Nature of the wavefront
Following his remarks on the propagation medium and the speed of light, Huygens gives a geometric illustration of the wavefront, the foundation of what became known as Huygens’ Principle. His principle of propagation is a demonstration of how a wave of light (or rather a pulse) emanating from a point also results in smaller wavelets:
...each of these waves can be infinitely feeble only as compared with the [primary wave], to the composition of which all the others contribute by the part of their surface which is most distant from [the wave’s origin]. This means that each particle in the ether is the source of a new wavefront, and although these “secondary wavelets” are characterized by Huygens as “feeble,” points on each wavelet collectively form the primary wave that is visible as light. The new wavefront, then, is the tangential surface to all the secondary wavelets in the direction of propagation. Critical to Huygens’s analysis is that these secondary wavelets can be mathematically constructed, allowing one to work backward from the secondary wavelets to construct a primary wave which has traveled for a certain time. This is the principle on which Huygens's entire theory of light turns, and it is what separates his theory from those of his predecessors.
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