Leonhard Euler and Thomas Young

The wave-theory was defended by:

• Franklin[8]
• the mathematician Leonhard Euler (b, 1707, d. 1783)

Euler published ‘Nova Theoria Laucis et Colorum’ [9] while living under the patronage of Frederic the Great at Berlin.

• He insisted strongly on the resemblance between light and sound: “light is in the aether the same thing as sound in air.”

Euler:

• accepted Newton’s doctrine that colour depends on wavelength
• supposed the frequency greatest for red light, and least for violet

But a few years later[10] he adopted the opposite opinion.

He explained how:

• material bodies appear coloured when viewed by white light
• the colours of thin plates are produced.

He denied that such colours are due to a more copious reflexion of light of certain particular periods.

He supposed that they represent vibrations generated within the body itself under the stimulus of the incident light.

According to this hypothesis, a coloured surface contains many elastic molecules.

• When agitated, these emit light of period depending only on their own structure.

Euler explained the colours of thin plates in the same way.

• The elastic response and free period of the plate at any place would depend on its thickness at that place.
• In this way, the dependence of the colour on the thickness was accounted for, the phenomena as a whole being analogous to well-known effects observed in experiments on sound.

An attempt to improve the corpuscular theory in another direction was made in 1752 by the Marquis de Courtivron,[11] and independently in the following year by T. Melvill.[12]

These writers suggested, as an explanation of the different refrangibility of different colours, that:

“the differently colour’d rays are projected with different velocities from the luminous body: the red with the greatest, violet with the least, and the intermediate colours with intermediate degrees of velocity.”

The amount of aberration would be different for every colour.

The satellites of Jupiter would change colour, from white through green to violet, through an interval of more than half a minute before their immersion into the planet’s shadow.

While at emersion the contrary succession of colours should be observed, beginning with red and ending in white.

Astronomers did not see this and so the hypothesis was abandoned.

Thomas Young

Thomas Young was born at Milverton in Somersetshire in 1773. He in medicine and began to write on optical theory in 1799.

His first paper[13] remarked that, according to the corpuscular theory, the speed of emission of a corpuscle must be the same in all cases, whether the projecting force be that of:

• the feeble spark produced by the friction of 2 pebbles, or
• the intense heat of the sun

This difficulty does not exist in the undulatory theory, since all disturbances are known to be transmitted through an elastic fluid with the same speed.

Some philosophers were reluctant to fill all space with an elastic fluid.

Young then shows the superior power of the wave-theory to explain reflexion and refraction.

In the corpuscular theory, it is difficult to see why part of the light should be reflected and another part of the same beam reflected.

But in the undulatory theory, there is no trouble, as is shown by analogy with the partial reflexion of sound from a cloud or denser stratum of air:

This is precisely the hypothesis adopted later by Fresnel and Green.

In 1801, Young made a discovery of the first magnitude[14] when attempting to explain Newton’s rings on the principles of the wave-theory.

He rejected Euler’s hypothesis of induced vibrations. Instead, he:

• assumed that all observed colours exist in the incident light.
• showed that they could be derived from it by a process used by Newton in his theory of the tides.[15]

Newton applied this principle to explain the anomalous tides at Batsha in Tonkin, which had previously been described by Halley.[16]

Young’s own illustration of the principle is evidently suggested by Newton’s.

Thus:

Young’s explanation of the colours of thin plates as seen by reflexion was, then, that the incident light gives rise to two beans which reach the eye: one of these beams has been reflected at the first surface of the plate, and the other at the second surface; and these two beams produce the colours by their interference.

One difficulty encountered in reconciling this theory with observation arose from the fact that the central spot in Newton’s rings (where the thickness of the thin film of air is zero) is black and not white, as it would be if the interfering beams were similar to each other in all respects.

To account for this Young showed, by analogy with the impact of elastic bodies, that when z light is reflected at the surface of a denser medium, its phase is retarded by half an undulation: so that the interfering beams at the centre of Newton’s rings destroy each other.

The correctness of this assumption he verified by substituting essence of sassafras (whose refractive index is intermediate between those of crown and flint glass) for air in the space between the lenses; as he anticipated, the centre of the ring-system was now white.

Newton had long before observed that the rings are smaller when the medium producing them is optically more dense.

Interpreted by Young’s theory, this definitely proved that the wave-length of light is shorter in dense media, and therefore, that its velocity is less. The publication of Young’s papers occasioned a fierce attack on him in the Edinburgh Review, from the pen of Henry Brougham, afterwards Lord Chancellor of England.

Young replied in a pamphlet which sold only 1 copy: There can be no doubt that Brougham for the time being achieved his object of discrediting the wave-theory.[19]

Young now turned his attention to the fringes of shadows.

In the corpuscular explanation of these, it was supposed that the attractive forces which operate in refraction extend their influence to some distance from the surfaces of bodies, and inflect such rays as pass close by. If this were the case, the amount of inflexion should obviously depend on the strength of the attractive forces, and consequently on the refractive indices of the bodies-a proposition which had been refuted by the experiments of s’Gravesande.

The cause of diffraction effects was thus wholly unknown, until Young, in the Bakerian lecture for 1803,[20] showed that the principle of interference is concerned in their formation.

When a hair is placed in the cone of rays diverging from a luminous point, the internal fringes (i.e. those within the geometrical shadow) disappear when the light passing on one side of the hair is intercepted.

His conjecture as to the origin of the interfering rays was not so fortunate.

He attributed the fringes outside the geometrical shadow to interference between the direct rays and rays reflected at the diffracting edge and supposed the internal fringes of the shadow of a narrow object to be due to the interference of rays inflected by the two edges of the object.

The success of so many developments of the wave-theory led Young to inquire more closely into its capacity for solving the chief outstanding problem of optics—that of the behaviour of light in crystals.

The beautiful construction for the extraordinary ray given by Huygens had lain neglected for a century; and the degree of accuracy with which it represented the observations was unknown.

At Young’s suggestion Wollaston,[21] investigated the matter experimentally.

He showed that the agreement between his own measurements and Huygeus’ rule was remarkably close.

Meanwhile the advocates of the corpuscular theory were not idle. In the next few years, a succession of discoveries on their part, both theoretical and experimental, seemed likely to imperil the good position to which Young had advanced the rival hypothesis.

The first of these was a dynamical explanation of the refraction of the extraordinary ray in crystals, which was published in 1808 by Laplace.[22]

His method is an extension of that by which Maupertuis had accounted for the refraction of the ordinary ray, and which since Maupertuis’ day had been so developed that it was now possible to apply it to problems of all degrees of complexity.

Laplace assumes that the crystalline medium acts on the light-corpuscles of the extraordinary ray so as to modify their velocity, in a ratio which depends on the inclination of the extraordinary ray to the axis of the crystal: 50 that, in fact, the difference of the squares of the velocities of the ordinary and extraordinary rays is proportional to the square of the sine of the angle which the latter ray makes with the axis.

The principle of least action then leads to a law of refraction identical with that found by Huygens’ construction with the spheroid; just as Maupertuis’ investigation led to a law of refraction for the ordinary ray identical with that found by Huygens’ construction with the sphere.

The law of refraction for the extraordinary ray may also be deduced from Fermat’s principle of least time, provided that the velocity is taken inversely proportional to that assumed in the principle of least action; and the velocity appropriate to Fermat’s principle agrees with that found by Huygens, being, in fact, proportional to the radius of the spheroid.

These results are obvious extensions of those already obtained for ordinary refraction.