Augustin Fresnel

Laplace’s theory was promptly attacked by Young,[23] who pointed out the improbability of such a system of forces required to impress the requisite change of velocity on the light-corpuscles.

Young’s paper failed to convince the contemporary world. But it permanently enriched science by proposing a dynamical foundation for double refraction on the principles of the wave-theory.

Young then proceeds to a formal proof that “an impulse is propagated through every perpendicular section of a lamellar elastic substance in the form of an elliptic undulation.”

This is the beginning of the dynamical theory of light in crystals.

Brewster[24] afterwards confirmed it when he found that compression in one direction causes an isotropic transparent solid to become doubly-refracting.

Meanwhile, in January 1808, the French Academy had proposed as the subject for the physical prize in 1810, “To furnish a mathematical theory of double refraction, and to confirm it by experiment.”

Among those who resolved to compete was Étienne Louis Malus (b. 1775, d. 1812), a colonel of engineers who had seen service with Napoleon’s expedition to Egypt.

While conducting experiments towards the end of 1808 in a house in the Rue des Enfers in Paris, Malus happened to analyse with a rhomb of Iceland spar the light of the setting sun reflected from the window of the Luxembourg, and was surprised to notice that the two images were of very different intensities.

Following up this observation, he found that light which bad been reflected from glass acquires thereby a modification similar to that which Huygens had noticed in rays which have experienced double refraction, and which Newton had explained by supposing rays of light to have “sides.”

This discovery appeared so important that without waiting for the prize competition he communicated it to the Academy in December, 1808, and published it in the following month.[25]

After this, Malus found that light which has been refracted at the surface of any transparent substance likewise possesses in some degree this property, to which he gave the name polarization.

His memoir[26], submitted to the Academy, contains a rich store of experimental and analytical work on double refraction.

It obtained the prize in 1810. Its immediate effect as regards the rival theories of the ultimate nature of light was to encourage the adherents of the corpuscular doctrine. It brought into greater prominence the phenomena of polarization, of which the wave-theorists, still misled by the analogy of light with sound, were unable to give any account.

The successful discoverer was elected to the Academy of Sciences, and became a member of tho celebrated club of Arcueil.[27]

But his health, which had been undermined by the Egyptian campaign, now broke down completely. He died at 36 in the following year.

The polarization of a reflected ray is in general incomplete i.e. the ray displays only imperfectly the properties of light which has been polarized by double refraction, but for one particular angle of incidence, which depends on the reflecting body, the polarization of the reflected ray is complete.

Malus measured with considerable accuracy the polarizing angles for glass and water, and attempted to connect them with the other optical constants of these substances, the refractive indices and dispersive powers, but without success.

The matter was afterwards taken up by David Brewster (b. 1781, d. 1868), who in 1815[28] showed that there is complete polarization by reflexion when the reflected and refracted rays satisfy the condition of being at right angles to each other.

Almost at the same time, Brewster made another discovery which profoundly affected the theory of double refraction.

It had till then beer believed that double refraction is always of the type occurring in Iceland spar, to which Huygens’ construction is applicable. Brewster now found this belief to be erroneous, and showed that in a large class of crystals there are two axes, instead of one, along which there is no double refraction.

Such crystals are called biaxal, the simpler type to which Iceland spar belongs being called uniaxal.

The wave-theory at this time was still encumbered with difficulties.

Diffraction was not satisfactorily explained.

• There was no explanation for polarization.
• The Huygenian construction appeared to require 2 different luminiferous media within doubly refracting bodies
  • The universality of that construction had been impugned by Brewster’s discovery of biaxal crystals.

The upholders of the emission theory were emboldened by the success of Laplace’s theory of double refraction.

In March 1817, they proposed Diffraction as the subject of the Academy’s prize for 1818. Within just 7 years, the corpuscular theory was completely overthrown.

Augustin Fresnel

The winner was Augustin Fresnel (b. 1788, d. 1827). He was:

• the son of an architect
• a civil engineer in the Government service in Normandy.

During the brief dominance of Napoleon after his escape from Elba in 1815, Fresnel fell into trouble for having enlisted in the small army which attempted to bar Napoleon’s return.

His arrest led to an enforced idleness which he used to study diffraction.

In his earliest memoir[29], he propounded a theory similar to that of Young, which was spoiled like Young’s theory by the assumption that the fringes depend on light reflected by the diffracting edge.

Observing, however, that the blunt and sharp edges of a knife produce exactly the same fringes, he became dissatisfied with this attempt, and

On July 15, 1816, he presented to the Academy a supplement to his paper[30]. For the first time, diffraction-effects are referred to their true cause—the mutual interference of the secondary waves emitted by those portions of the original wave-front which have not been obstructed by the diffracting.

Fresnel’s method of calculation utilized the principles of both Huygens and Young.

He summed the effects due to different portions of the same primary wave-front, with due regard to the differences of phase engendered in propagation.

The earliest memoir, which had been presented to the Academy in the autumn of 1815, had been referred to a Commission of which the reporter was François Arago (b. 1786, d. 1853). Arago was so much impressed that he sought the Fresnel’s friendship. He eventually became Fresnel’s strenuous champion.

A champion was needed when the larger memoir was submitted.

The Commission was largely made up of Laplace, Poisson, and Biot.

• They were all zealous supporters of the corpuscular theory.

During the examination, however, Fresnel was vindicated in a curious way.

He had calculated in the mernoir the diffraction-patterns of a straight edge, of a narrow opaque body bounded by parallel sides, and of a narrow opening bounded by parallel cdges, and had shown that the results agreed excellently with his experimental measures.

Poisson, when reading the manuscript, happened to notice that the analysis could be extended to other cases, and in particular that it would indicate the existence of a bright spot at the centre of the shadow of a circular screen.

He suggested to Fresnel that this and some further consequences should be tested experimentally; this was done, and the results were found to confirm the new theory.

The concordance of observation and calculation was so admirable in all cases where a comparison was possible that the prize was awarded to Fresnel without further hesitation.

In the same year in which the memoir on diffraction was submitted, Fresnel published an investigation[32] of the influence of the earth’s motion on light.

We have already seen that aberration was explained by its discoverer in terms of the corpuscular theory, and it was Young who first showed[33] how it may be explained on the wave-hypothesis. “Upon considering the phenomena of the aberration of the stars,” he wrote, “I am disposed to believe that the luminiferous aether pervades the substance of all material bodies with little or no resistance, as freely perhaps as the wind passes through a grove of trees.”

In fact, if we suppose the aether surrounding the earth to be at rest and unaffected by the earth’s motion, the light-waves will not partake of the motion of the telescope, which we may suppose directed to the true place of the star, and the image of the star will therefore be displaced from the central spider-line at the focus by a distance equal to that which the earth describes while the light is travelling through the telescope. This agrees with what is actually observed.

But a host of further questions now suggest themselves. Suppose, for instance, that a slab of glass with a plane face is carried along by the motion of the earth, and it is desired to adjust it so that a ray of light coming from a certain star shall not be bent when it enters the glass: must the surface be placed at right angles to the true direction of the star as freed from aberration, or to its apparent direction as affectedly aberration?