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The Wave Theory of Light

IntroductionThe recognition of the wave nature and mode of propagation of light permits a

more fundamental approach to the explanation of optical effects than is possible using

only more limited assumptions of geometrical optics. The rectilinear propagation of

light in a uniform medium, which is the sole basis of the geometrical approach to

optical systems, is from the standpoint of wave optics, only an approximation, which

nevertheless is sufficiently closely true in the circumstances of use of many optical

instruments in terms of “rays” of light is, therefore, in many respects quite adequate.

The introduction of the concept of light waves leads in such cases to results which

include and agree with those arrived at, by geometrical methods, but some important

details and refinements in the understanding of the effects occurring are added when

this more comprehensive approach is used.

Another class of optical effects is, however, entirely beyond the range of

description by simple geometrical methods. This includes such phenomena as

interference, diffraction, polarization and dispersion of light; and the assumption that

light is propagated in waves is essential to any explanation of these matters.

Interference and diffraction of light become apparent in more especial circumstances

than those for which the geometrical methods are, and the most familiar forms of these

phenomena are those characteristic of the shapes and sizes of apertures through which

light beams are allowed to pass. Essentially similar effects are manifested by all types

of waves, as e.g., by sound waves, waves on the surface of water, as well as by light

waves. Optical polarization and dispersion effects, on the other hand, depend for their

explanation on the particular character of light waves. The details of the observed

phenomena of this kind are only satisfactorily accounted for on the assumption that

light waves are transverse and electromagnetic in nature.

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Discussion of the methods used and the results obtained, at least for a

representative selection of the many experiments on optical effects of this kind, and of

the manner in which the wave theory is able to explain such observations and the

extent to which it does so satisfactorily, must necessarily occupy a portion of any

account of wave optics. A further important section must be devoted to description of

practical applications based on these effects, including the principles and uses of

instruments such as interferometers, gratings and polarimeters.

The present course deals with the phenomena of interference, diffraction,

polarization and dispersion of light. A representative selection of material is made,

with the object of elucidating basic principles, and the kinds of practical applications

of the effects are discussed.

Outline of the wave optics historyThe history of the development of wave optics opens with a small group of

experimental observations made during the latter half of the seventeenth century.

Several wave-optical phenomena of diverse kinds were then discovered, and, since the

effects were in most cases merely observed without any satisfactory explanation being

possible, their interconnection was not clearly evident at the time. The principal names

associated with this early period are those of Grimaldi, Hooke, Bartholinus, Huygens

and Newton. During the following century observations of a similar character were

reported by various workers, but no marked advance in the explanation of the observed

phenomena was made. A really satisfactory understanding, on wave-optical principles,

of the various observed effects began to be developed soon after the commencement of

the nineteenth century. This second major period of advance opened with the vital

work of Young and Fresnel, along with several other investigators of the nineteenth

century must be mentioned as having made contributions of special value towards a

rapidly deepening understanding of the fundamentals of the subject.

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Reference will be made in turn to important contributions made by prominent

investigators untill towards the close of the nineteenth century, when a basic

understanding of wave optics (especially of interference and diffraction) may be said

to have been well established. Detailed developments, since this time, of theoretical

and experimental aspects of interference and diffraction are too numerous and

complex for inclusion in a brief outline.

Grimaldi studied intensity variations near the edges of shadows of obstacles.

Objects such as fine hairs, rectangular corners of opaque bodies, etc., were essentially

Fresnel diffraction patterns; some of these were complex since the objects were not

always of a simple kind. The work was published in 1665, two years after Grimaldi’s

death. Hooke reported observations of a similar nature in 1672, and also performed

some experiments on white-light fringes with thin films. Meanwhile (1669)

Bartholinus discovered the property of a calcite crystal of forming a double image

when a single object is viewed, through it. The phenomenon of double refraction,

discovered in this way, awaited the concept of transverse light waves and the

polarization of light for its explanation.

Huygens performed experiments of a more systematic kind on double refraction;

his best-known contribution to wave optics is, however, his explanation of rectilinear

propagation assuming the wave nature of light. He used his principle of secondary

waves to account for reflection and refraction phenomena, and also extended this to a

partial explanation of double refraction, assuming ellipsoidal forms for the

extraordinary wave-fronts. He also had some understanding that transverse waves

were a necessary supposition for the explanation of this phenomenon.

In the field of optics Newton’s best-known work is perhaps that on dispersion

and the composition of white light. His advocacy of the corpuscular theory of light,

and his controversy with Huygens, are also well known. All the elementary wave-

optical effects had at that time been observed, Newton’s being a further example of

effects of the interference type then known. Attempts at explanation of these effects in

terms of the corpuscular theory were made by Newton’s; none of these explanations

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was satisfactory, but most of the observations were not then accounted for on the basis

of the wave nature of light, and the wave, theory seemed untenable to Newton because

of the known non-rectilinear effects obtained with other kinds of waves. Newton’s

“optics” appeared in 1704, and the corpuscular theory remained in the ascendancy

during the ensuing century. The high respect accorded to Newton’s views was partly

responsible for this.

Though the implications of their results were by no means immediately

accepted, the revival of the wave theory is mostly attributable to the researches in

optics performed by Young (1801-4) and by Fresnel (1815-26). Young conceived the

idea of interference of waves as a result of study of acoustical effects in the first place.

He was able ultimately to produce similar effects with light, though on a very different

scale, the best known of which is the double-slit interference experiment. The

corpuscular theory had no real explanation for these results, whereas their explanation

on the principle of superposition, introduced by Young, was fairly clear. This revival

of the wave theory of light propagation met with considerable resistance at first, and it

was only becoming well established after a considerable amount of work had also been

performed by Fresnel. Fresnel, without knowledge of Young’s earlier work, used the

principle of superposition in explanation of his observation on diffraction and really

laid the essential basis of diffraction theory. He realized that this principle of

superposition could be applied to all the waves from the extended distribution of

secondary sources, which, according to Huygens’ principle, constitute the wavefront

passed by any aperture. Explanation of diffraction patterns formed by a large variety of

aperture and obstacles were immediately possible and the correspondence between

prediction and experiment confirmed in many cases. At the same time the basis of

Huygens’ construction of advancing wave-fronts beam clearer, unrestricted wave-

fronts only producing strictly rectilinear propagation, and diffraction effects arising

because of the apertures through which the waves necessarily have to pass. Though

certain assumptions introduced by Fresnel awaited later justification by more

comprehensive theories of diffraction (by Stokes, Kirchoff, and others), use of the

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ideas introduced by Fresnel remains adequate for the prediction and general

understanding of most simple diffraction effects.

The discovery by Malus (in 1808) of the polarization by reflection of light at an

appropriate angle of incidence upon a glass plate (and the possibility of using two

glass plates in this way as polarizer and analyzer) provided vital information leading to

understanding of the nature of light waves. After some time, and despite oppostion to

his view, Fresnel gradually realized that this effect found its true explanation in the

fact that transverse waves were involved in the propagation of light. He developed the

elastic solid theory, in which the waves were imagined as transverse vibrations in the

ether, which was considered as an all-pervading elastic material. The Fresnel equations

(which explain relative transmitted and reflected light amplitude at interfaces between

optical media) were deduced in this way; much later they were shown to be obtainable

from the electromagnetic theory of light, in a manner which was more satisfactory in

some details.

The understanding of interference and diffraction effects gained in this period,

made possible determinations of light wavelength. Fraunhofer (around 1821), besides

making diffraction observations, developed grating production methods and

spectroscopic techniques, which, along with his discovery of the absorption lines in the

solar spectrum, made possible more accurate measurements on dispersive properties of

materials.

The advances in the understanding of electrical and magnetic phenomena

associated with such names as Oersted, Ampere, Faraday and Henry, etc., were also

taking place more or less simultaneously. The understanding of these effects together

with confirmatory evidence provided by the discovery of the Faraday magneto-optical

effects (1845), and the Kerr electro-optical effect (1865), provided the basis of the

electromagnetic theory of light, introduced by Maxwell (1864). Velocity of light

measurements by Fizeau (1849) and Foucault (1850), of higher accuracy than the

earlier determinations by Romer (1676) and Beadley (1727), provided supporting

evidence. The possibility of obtaining the velocity of light in various media (e. g., in

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water, as well as in air and in vacuo) arose along with the development of these

terrestrial methods; and the relative velocities in different media gave support to the

wave mode of propagation. The velocity expected from Maxwell’s theory was

confirmed, especially by the more accurate determinations, first in air and later in

vacuo, made by methods later developed by Michelson. The artificial production of

electromagnetic radiation, by Hertz, and the confirmation that its velocity was the

same as that of light, and thus in agreement also with the predictions of the theory,

came twenty-three years after the actual theory.

The work of Cauchy (1836) and Sellmeler (1871), which opened the

development of dispersion theory, also belongs to the period under survey. Really

rapid development in the understanding of matters such as absorption and dispersion

came only after the establishment of the electromagnetic theory.