John William Strutt

“ If the light reflected from a plate of any thickness be examined with a spectroscope of sufficient resolving power, the spectrum will be traversed by dark bands, of which the centre corresponds to those wave-lengths which the plate is incompetent to reflect. It is obvious that there is no limit to the fineness of the bands which may be thus impressed upon a spectrum, whatever may be the character of the original mixed light. ”

“ In a classical experiment interference-bands were employed to examine whether light moved faster or slower in glass than in air. For this purpose a very thin piece of glass may be interposed in the path of one of the interfering rays, and the resulting displacement of the bands is such as to indicate that the light passing through the glass is retarded. In a better form of the experiment two pieces of parallel glass cut from the same plate are interposed between the prism and the screen, so that the rays from O1 (fig. 1) pass through one part and those from O2 through the other. ”

“ In practice, the source is an elongated slit, whose direction requires to be carefully adjusted to parallelism with the reflecting surface or surfaces. By this means an important advantage is gained in respect of brightness without loss of definition, as the various parts of the aperture give rise to coincident systems of bands.
The question of the admissible width of the slit requires consideration. We will suppose that the light issuing from various parts of the aperture is without permanent phase-relations, as when the slit is backed immediately by a flame, or by an incandescent filament. ”

“ In consequence, however, of the fact that the range of sensitiveness of the eye is limited to less than an “octave,” the centre of the first dark band (on either side) is sensibly black, even when white light is employed; but it should be carefully remarked that the existence of even one band is due to selection, and that the formation of several visible bands is favoured by the capability of the retina to make chromatic distinctions within the visible range.
The number of perceptible bands increases pari passu with the approach of the light to homogeneity. ”

“ When an undulation is transmitted through a surface terminating different mediums, it proceeds in such a direction that the sines of the angles of incidence and refraction are in the constant ratio of the velocity of propagation in the two mediums.
(vi.) When an undulation falls on the surface of a rarer medium, so obliquely that it cannot be regularly refracted, it is totally reflected at an angle equal to that of its incidence. ”

“ According to mechanical principles the second reflection involves a change of sign, equivalent to a gain or loss of half an undulation. When a series of waves constituting any particular coloured light is reflected from an infinitely thin plate, the two partial reflections are in absolute discordance and, if of equal intensity, must give on superposition complete darkness. With the aid of this principle the sequence of colours in Newton’s rings is explained in much the same way as that of interference fringes (above, § 5) . ”

“ The fundamental experiment is as follows. At the centre of curvature of a concave looking-glass, quicksilvered behind, is placed an opaque card, perforated by a small hole through which sunlight is admitted. The main body of the light returns through the aperture; but a series of concentric rings are seen upon the card, the formation of which was proved by Newton to require the co-operation of the two surfaces of the mirror. Thus the diameters of the rings depend upon the thickness of the glass, and none are formed when the glass is replaced by a metallic speculum. ”

“ A white stripe may thus be formed in a situation where without the prism the mixture of colours would be complete, so far as could be judged by the eye.
The simplest case that can be considered is when the “thin plate” is bounded by plane surfaces inclined to one another at a small angle. By drawing back the prism (whose edge is parallel to the intersection of the above-mentioned planes) it will always be possible so to adjust the effective dispersing power as to bring the nth bars to coincidence for any two assigned colours, and therefore approximately for the entire spectrum. ”

“ At this angle of refraction, and with this kind of glass, the retardation of phase is accordingly nearly independent of wave-length, and therefore the bands formed, as the thickness varies, are approximately achromatic. Perfect achromatism would be possible only under a law of dispersion
μ2 = A′ − B′λ2. If the source of light be distant and very small, the black bands are wonderfully fine and numerous. The experiment is best made (after Newton) with a right-angled prism, whose hypothenusal surface may be brought into approximate contact with a plate of black glass. ”

“ Newton experimented especially with thin plates of air enclosed by slightly curved glasses, and the coloured rings so exhibited are usually called after him “Newton’s rings.”
The colours are manifested in the greatest purity when the reflecting surfaces are limited to those which bound the thin film. This is the case of the soap-bubble. When, as is in other respects more convenient, two glass plates enclosing a film of air are substituted, the light under examination is liable to be contaminated by that reflected from the outer surfaces. ”

“ The spectrum which is allowed to pass is the proximate source of light in the interference experiment, and since the deviation of any colour from the central white image is proportional to λ, it is only necessary to arrange the mirror so that its plane passes through the white image in order to realize the conditions for the formation of achromatic bands. ”

“ If the range of wave-length included be 1/50000, a corresponding number of interference fringes may be made visible. The above was the number obtained by A. H. L. Fizeau. Using vacuum tubes containing, for example, mercury or cadmium vapour, A. A. Michelson has been able to go much farther. The narrowness of the bright line of light seen in the spectroscope, and the possibility of a large number of Fresnel’s bands, depend upon precisely the same conditions; the one is in truth as much an interference phenomenon as the other. ”

“ The magnitude of the force corresponds to the amplitude of the vibration, and the inclination of the force corresponds to the phase. A group of forces, of equal intensity, represented by lines drawn from the centre to the angular points of a regular polygon, constitute a system in equilibrium. Consequently, a system of vibrations of equal amplitude and of phases symmetrically distributed round the period has a zero resultant. ”

“ We may then conveniently discard the idea of phase, and regard the amplitudes as at random positive or negative. If all the signs are the same, the intensity is n2; if, on the other hand, there are as many positive as negative, the result is zero. But, although the intensity may range from 0 to n2, the smaller values are much more probable than the greater. ”

“ Rays diverging from a soda flame at E are rendered parallel by the lens, and after reflection from the surfaces are recombined by the lens at E. To make an observation, the coincidence of the radiant point and its image must be somewhat disturbed, the one being displaced to a position a little beyond, and the other to a position a little in front of the diagram. The eye, protected from the flame by a suitable screen, is placed at the image, and being focused upon AB, sees the field traversed by bands. ”

“ For actual experiment when, as usually happens, it is desirable to economize light, the point may be replaced by a line of light perpendicular to the plane of the diagram, obtained either from a linear source, such as the filament of an incandescent electric lamp, or by admitting light through a narrow vertical slit. ”

“ In this way the idea of the intensity of a luminous source, independently of any questions of phase, is seen to be justified, and we may properly say that two candles are twice as bright as one.
§ 5. Interference Fringes.—In Fresnel’s fundamental experiment light from a point O (fig. 1) falls upon an isosceles prism of glass BCD, with the angle at C very little less than two right angles. The source of light may be a pin-hole through which sunlight enters a dark room, or, more conveniently, the image of the sun formed by a lens of short focus (1 or 2 in.) ”

“ In this way the advantage of narrowing the bright rings is attained in great measure without too heavy a sacrifice of light. The plate in the optical sense is one of air, and is bounded by plates of glass whose inner silvered surfaces are accurately flat and parallel. The outer surfaces need only ordinary flatness, and it is best that they be not quite parallel to the inner ones. The arrangement constitutes a spectroscope, inasmuch as it allows the structure of a complex spectrum line to be directly observed. ”

“ The plane parallel plates A and B are worked originally in one piece, which is afterwards cut in two. The two pieces are placed parallel to one another, thus ensuring exact equality in the two optical paths AC and AD” (see Michelson, Light-Waves and their Uses, Chicago, 1903) .
The adjustments of this apparatus are very delicate. Of the fully silvered mirrors C, D, the latter must be accurately parallel to the image of the former. For many purposes one of the mirrors, C, must be capable of movement parallel to itself, usually requiring the use of very truly constructed ways. ”

“ We have not proved that when n is large there is any tendency for a single combination to give the intensity equal to n, but the quite different proposition that in a large number of trials, in each of which the phases are rearranged arbitrarily, the mean intensity will tend more and more to the value n. ”

“ This may be regarded as the definition; and then experiment may be appealed to to prove that the intensity of light from a given source varies inversely as the square of the distance. But our conviction of the truth of the law is perhaps founded quite as much upon the idea that something not liable to loss is radiated outwards, and is distributed in succession over the surfaces of spheres concentric with the source, whose areas are as the squares of the radii. The something can only be energy ”

“ In such a case the system of bands is achromatic, and the heterogeneity of the light is no obstacle to the formation of visible bands of high order.
These requirements are very easily met by the use of Lloyd’s mirrors, and of a diffraction grating (see Diffraction) with which to form a spectrum. White light enters the dark room through a slit in the window-shutter, and falls in succession upon a grating and an achromatic lens, so as to form a real diffraction spectrum, or rather a series of such, in the focal plane. ”

“ Haidinger’s Rings dependent on Obliquity.—It is remarkable that the well-known theoretical investigation, undertaken with the view of explaining Newton’s rings, applies more directly to a different system of rings discovered at a later date.
The results embodied in equations (1) to (8) have application in the first instance to plates whose surfaces are absolutely parallel, though doubtless they may be employed with fair accuracy when the thickness varies but slowly. ”

“ The combination lends itself to projection and the pattern seen upon the screen is very beautiful if proper precautions are taken to eliminate the white light reflected from the first and fourth surfaces of the plates (see Nature, 1901, 64, 385) .
Theory and observation alike show that the transmitted colours of a thin plate, e.g. a soap film or a layer of air, are very inferior to those reflected. Specimens of ancient glass, which have undergone superficial decomposition, on the other hand, sometimes show transmitted colours of remarkable brilliancy. ”

“ For study of the colours of thin plates there are no more interesting subjects than the soap-film. For projection the films may be stretched across vertical rings of iron wire coated with paraffin. In their undisturbed condition they thin from the top, and the colours are disposed in horizontal bands. ”

“ The fact that two surfaces can be made to fit another in all azimuths proves that they are spherical and of equal curvatures, but one convex and the other concave, the case of perfect flatness not being excluded. ”

“ The first thing to be noticed is that, when α approaches the critical angle, cosα′ becomes as small as we please, and that consequently the retardation corresponding to a given thickness is very much less than at perpendicular incidence. Hence the glass surfaces need not be so close as usual.
A second feature is the increased brilliancy of the light. According to (7) the intensity of the reflected light when at a maximum (sin 1/2κγ = 1) is 4e2/ (1 + e2) 2. At perpendicular incidence e is about 1/5, and the intensity is somewhat small ”

“ The sensation of different colours depends on the different frequency of vibrations excited by the light in the retina.
(iv.) All material bodies have an attraction for the aethereal medium, by means of which it is accumulated in their substance, and for a small distance around them, in a state of greater density but not of greater elasticity. ”

“ It would seem that the eye is but little sensitive to colours thus presented, perhaps on account of its own want of achromatism.
§ 7. Airy’s Theory of the White Centre.—If a system of Fresnel’s bands be examined through a prism, the central white band undergoes an abnormal displacement, which has been supposed to be inconsistent with theory. The explanation has been shown by Airy (Phil. Mag., 1833, 2, p. 161) to depend upon the peculiar manner in which the white band is in general formed. ”