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. The probable explanation, suggested by Brewster, is that we have here to deal not merely with one, but with a series of thin plates of not very different thicknesses. It is evident that with such a series the transmitted colours would be much purer, and the reflected much brighter, than usual. If the thicknesses are strictly equal, certain wave-lengths must still be absolutely missing in the reflected light; while on the other hand a constancy of the interval between the plates will in general lead to a special preponderance of light of some other wave-length for which all the component parts as they ultimately emerge are in agreement as to phase.
On the same principle are doubtless to be explained the colours of fiery opals, and, more remarkable still, the iridescence of certain crystals of potassium chlorate. Stokes showed that the reflected light is often in a high degree monochromatic, and that it is connected with the existence of twin planes. A closer discussion appears to show that the twin planes must be repeated in a periodic manner (Phil. Mag., 1888, 26, 241, 256; also see R. W. Wood, Phil. Mag., 1906).
A beautiful example of a similar effect is presented by G. Lippmann’s coloured photographs. In this case the periodic structure is actually the product of the action of light. The plate is exposed to stationary waves, resulting from the incidence of light upon a reflecting surface (see [Photography]).
All that can be expected from a physical theory is the determination of the composition of the light reflected from or transmitted by a thin plate in terms of the composition of the incident light. The further question of the chromatic character of the mixtures thus obtained belongs rather to physiological optics, and cannot be answered without a complete knowledge of the chromatic relations of the spectral colours themselves. Experiments upon this subject have been made by various observers, and especially by J. Clerk Maxwell (Phil. Trans., 1860), who has exhibited his results on a colour diagram as used by Newton. A calculation of the colours of thin plates, based upon Maxwell’s data, and accompanied by a drawing showing the curve representative of the entire series up to the fifth order, has been given by Rayleigh (Edin. Trans., 1887). The colours of Newton’s scale are met with also in the light transmitted by a somewhat thin plate of doubly-refracting material, such as mica, the plane of analysis being perpendicular to that of primitive polarization.
The same series of colours occur also in other optical experiments, e.g. at the centre of the illuminated area when light issuing from a point passes through a small round aperture in an otherwise opaque screen.
The colours of which we have been speaking are those formed at nearly perpendicular incidence, so that the retardation (reckoned as a distance), viz. 2μt cos α′, as sensibly independent of λ. This state of things may be greatly departed from when the thin plate is rarer than its surroundings, and the incidence is such that α′ is nearly equal to 90°, for then, in consequence of the powerful dispersion, cos α′ may vary greatly as we pass from one colour to another. Under these circumstances the series of colours entirely alters its character, and the bands (corresponding to a graduated thickness) may even lose their coloration, becoming sensibly black and white through many alternations (Newton’s Opticks, bk. ii.; Fox-Talbot, Phil. Mag., 1836, 9, p. 40l). The general explanation of this remarkable phenomenon was suggested by Newton.
Let us suppose that plane waves of white light travelling in glass are incident at angle α upon a plate of air, which is bounded again on the other side by glass. If μ be the index of the glass, α′ the angle of refraction, then sin α′ = μ sin α; and the retardation, expressed by the equivalent distance in air, is
2t sec α′ − μ·2t tan α′ sin α = 2t cos α′;
and the retardation in phase is 2t cos α′/λ, λ being as usual the wave-length in air.
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.