
....Optics Highlights  

V. Ray Optics, Corpuscles and Waves 

Ray optics may be said to have begun as a science with the discovery of the law of refraction by Willebrord Snell in 1621 and its description in mathematical terms by René Descartes in 1637. In 1657, Fermat showed that the law is consonant with the "principle of least time," with light traveling more slowly in the denser medium. (Onehundred and seventy years later, William Hamilton used this principle as a basis for a general mathematical theory of ray optics). During 166566, Newton conducted the refraction experiments which led to his theory of colors (1672). Although Newton based his explanations of reflection and refraction on a corpuscular theory of light, he was the first to demonstrate an optical periodic phenomenon (Newton’s rings). Huygens accepted the need for a mechanical theory of light, but his explanations (1690) of refraction and reflection were based completely on the concept of wavelets, secondary wave fronts. The comprehensive explanations of Newton, his great reputation, and the discovery of the aberration of starlight and the first measurement of the speed of light by James Bradley in 1725 strengthened the general belief in the corpuscular theory, but Leonhard Euler, Benjamin Franklin, and a few others rejected it. Euler based his theory of light (1768) on the vibrations of a pervasive fluid, the ether.  
Willebrord Snell (15801626) switched from the study of law to mathematics. and he eventually succeeded his father as professor of mathematics at the University of Leiden. Although he discovered the law of refraction, he did not publish the result and his priority was not recognized until Huygens mentioned Snell’s discovery in his work some seventy years later.  
René Descartes (15961650) was the great philosopher and mathematician of the first half of the 17^{th} century. Although he was nominally a Roman Catholic and held rank in the lower nobility, he spent much of his adult life outside of France, principally in the Protestant low countries, seemingly in fear of the persecutions of heretics that swept France. Indeed, his works were put on the proscribed list shortly after his death. Cartesian physics was mechanistic and deterministic, all matter and light consisted of infinitely divisible substances, set into initial vorticelike motion by God. Light was described as consisting of tiny globes that travel and bounce according to the laws of optics; color was due to the different spins of the globes.  
Pierre de Fermat (16011665) the son of a leather merchant, studied law at the University of Toulouse and worked as a lawyer and councilor to the local parliament in Toulouse. He devoted his free time to mathematics. He only published one minor paper, and his work in number theory, probability, and geometry would have been lost had his son not published his letters and notes after his death. Fermat corresponded with both Descartes and Pascal. It is said that Descartes was enraged when he sent him his work on the principle of least time and criticized Descartes work on optics, which was based on the assumption that light travels faster in a denser medium.  
(Sir) William Rowan Hamilton (18051865) was a child prodigy in languages and mathematics who submitted his first paper to the Royal Irish Academy when he was 17. He entered Trinity College where, at 22 , he was elected a professor in astronomy and royal astronomer of Ireland while still an undergraduate. He invented quarternions, breaking with the tradition of commutative algebras and discovered conical refraction, but his great contribution to ray optics, based on the work of Fermat, was the least action principle. Hamilton wrote poetry, ignoring the advice of his friend, William Wordsworth, to stick to mathematics. Problems in his marriage in later life (his wife was a semiinvalid) led, apparently, to a diet of alcohol and mutton chops which probably contributed to his death from gout.  
James Bradley (16931762) was the third Astronomer Royal, following Flamsteed and Halley. He was introduced to Halley by his uncle, a vicar and amateur astronomer who tutored him in astronomy; he himself entered the church as vicar of Bridstow and also held a sinecure as an absentee parish rector for a couple of years. He left the church when he received a professorship at Oxford. Bradley’s observation of the aberration of starlight by the earth’s motion put the quietus to the last diehard belief that the earth was stationary.  
Leonhard Euler (17071783) was the most productive mathematician of all time; a projected edition of his collected works will comprise 72 volumes. He also had thirteen children. Euler was born in Switzerland, but went with the Bernouli’s to St. Petersburg where he served for three years in the Russian navy and remained most of his life as a professor of mathematics, excepting a contentious 25 year period he spent in Prussia at the court of Frederick the Great. He lost one eye at 31 and was almost completely blind due to a cataract after age 58; still, he completed almost half his work after that time. Euler was one of the few to reject the corpuscular theory and Newton’s assertion that an achromatic lens was impossible. He based his argument on the fact that the eye contained an achromatic lens.  
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