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Parabolic mirrors reflect light while glass prisms both reflect and refract it, depending on the angle at which the light beam strikes the material. Understanding the behaviour of light in glass requires knowledge of light, combined with expertise in glass manufacture, and very few individuals or firms in Britain or Europe possessed both. Rene Descartes pioneered the science of optics – where the study of light and vision come together. Newton’s Optics, published in 1704, took Descartes further by showing that white light was a combination of colours that could be separated into the spectrum by refraction through prisms or lenses. The Newtonian corpuscular theory proposed that light was made up of a stream of particles or corpuscles, and this remained the consensus for nearly 100 years until a new wave theory began to gain ground, led by Scotsman Thomas Young and Augustin Fresnel. What makes the corpuscular and wave theories of light important to this story is that Sir David Brewster, who, simultaneous to French physicist Etienne-Louis Malus, first described polarization and invented the kaleidoscope, was a big admirer and biographer of Newton. For this he was stigmatized by some other natural philosophers, and for his slow acceptance of Fresnel’s wave theories, which was due to his long-standing rivalry with Fresnel over the invention of the dioptric lens.

Theories of light, its properties and behaviour, are central to an understanding of lighthouse optics and James Chance mastered these from an early age. By the time he entered Trinity College, Cambridge in 1833, the corpuscular and wave theories had been unified, though words such as ‘ether’ were still in common parlance notwithstanding its somewhat vague meaning. It is worth going into some detail on the subject because later discussion on lenses, reflection and refraction will become clearer. It seems appropriate to reproduce here in Chance’s own words what light is and how it behaves. These writings are taken from a series of lectures he gave in the late 1840s at technical schools near Birmingham supported by Chance Brothers, who had an interest in securing a good supply of trained technicians for their glass factory.

Sir Isaac Newton … succeeded in decomposing light into its elementary colours and laid the foundation for the science of optics … the basis from which subsequent philosophers such as Young, Fresnel, Arago and Brewster have deduced the most remarkable consequences, such as to exceed our belief were they not the result of mathematical demonstration.

The science of optics is one of vast practical importance. To this we owe the telescope and the microscope, the one extending our vision into the remotest bounds of space, the other disclosing to us animated matter whose space itself had seemed to vanish, each revealing to us new wonders of creation, of which we should have been entirely ignorant ‘giving us’ as Herschel says ‘the glance of the eagle and the scrutiny of the insect’.

… Everyone must have noticed the waves, either of the sea, or of some large body of water, how the whole surface is in motion without any advance (except from tides) of the water itself; or how when a stone is thrown into a still surface of water, the little waves, starting from the point where the stone strikes the water as a centre spread out in successive circles, or again, now as before harvest-time, when the wind is high the whole surface of a cornfield seems to be advancing in the direction of the wind: now in each of these instances motion itself is transmitted through long distances, while particles themselves which we successively find in motion merely vibrate to and fro within narrow limits. In a similar manner, then, the sensation of light is produced upon our eye – the ether, pervading all space, is set in motion by the sun, or another luminary, just as the sea or the cornfield wave before the wind.

… The velocity with which light travels – i.e. with which the state of vibration is communicated from one point to the succeeding one, is at the amazing rate of roughly 200,000 miles per second. And yet, after explaining that this is the velocity of the communication of motion, and not any particle itself, it will appear to be less inconceivable the Electric telegraph appears a beautiful example of the communication of motion; we know by daily experience that the length of time that transmission is so inappreciable as to seem instantaneous: and so when we are looking at the sun we may readily suppose that luminary to be acting upon one end of a line of ethereal particles and that the vibration thus transmitted to the membrane of our eye corresponds to the magnetic needle at the termination of the wire of an electric telegraph.

David Brewster was a leading light in optical science and Chance includes him in his list alongside Young, Fresnel and Arago. Brewster was the first British optical scientist to recognize the value of optical science to lighthouse illumination. By the 1820s he had been showered with all the academic prizes on offer. He was Britain’s most revered optical scientist, almost on a par with Fresnel and Malus in France. Malus had first described the polarization of light in 1808, in which light is sent in a straight line, and Brewster at the same time came up with the same idea, which he called Brewster’s Law – the angle of incidence for which the polarisation is complete is given by tan = n, where n is the refractive index of the reflective medium. In 1817, Young realized that polarization could be accommodated in a wave theory of light. Fresnel arrived independently at the same conclusions, and it was largely his genius that took the wave theory to the point where it accounted for all the facts concerning reflection, refraction, defraction, interference, polarization and double refraction, and could be used to predict different phenomena. In his review of Brewster’s legacy to science, William Cochrane, a contributor to a symposium held in 1981 to commemorate the bicentenary of Brewster’s birth, states that Brewster’s attitude to Fresnel’s theory, which he called ‘undulatory theory’, was at best agnostic, he avoided using it and that Brewster did not expound on it in his 1831 Treatise on Optics where he noted that ‘the undulatory theory has been received by many of our most distinguished philosophers and adopted even by those who do not admit it as a physical truth.’ (It is interesting to note, by the way, that Chance also uses the word ‘undulatory’ when describing the behaviour of light particles.) Nevertheless, Brewster’s scepticism did not retard his application of these theories to lighthouse optics.

The refractive index is an important measure in lighthouse optics because it describes how light behaves in different materials, as was shown by Chance in the same lecture, when he described how light changes direction when it enters a body of water. It is the value that is found by dividing the speed of light (186,000 miles (300km) per second) in a vacuum by the speed of light in a second medium, such as glass. The value determines the amount a ray of light will be deflected as it travels from a vacuum into another medium. The index of refraction in a vacuum, and in air to all intents and purposes, is 1. Brewster’s 1813 Treatise on Optics goes into great detail about the refractive indices of light in more than 100 materials, including egg white and flint. Some of the more important for our purposes are:

Chromate of lead	2.974
Glass, lead 3, flint 1	2.028
Glass, lead 1, flint 1	1.787
Bottle glass	1.582
Plate glass	1.542–1.514
Crown glass	1.534–1.525
Water	1.336

Fresnel used crown glass in his lenses because it was easier to make than the more refractive flint glass, which was preferred by Brewster. Though Brewster’s inventive and theoretical genius was never disputed, his reputation later declined because he seldom interpreted his observations within an acceptable theoretical framework. This was done by others, and the connection with Brewster has sometimes been lost, as is most obviously demonstrated in the question of dioptric lenses. His personality also often brought him into conflict with his peers, and by the 1830s he was regarded very much as an anti-establishment figure – the establishment being the Tory-dominated institutions of government, church and academia, particularly Cambridge University where much of the theoretical work was being done. J.B. Morrell, another contributor to the 1981 Brewster symposium, in his account of Brewster’s work, noted his despair at the decline of science and his proposal to form an association of nobility, clergy, gentry and philosophers to remedy the depressed state of British science. Interesting for his insight into the feud between Brewster and the Stevensons, Morrell was particularly careful when exploiting Brewster’s retrospective public accounts of events and communications: ‘We found them very stimulating for their polemical perceptions and acute insights, but wherever possible they were checked against published and unpublished contemporary documents.’ Any treatment of Brewster’s writings (not least, this one) has to dig beneath the surface.