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pended in the liquid. If this be then placed in a glass trough with parallel sides, and a beam of sunlight be sent through it and received on a screen 15 to 20 feet distant, the image has a deep yellow color. The liquid itself presents a rich blue tint. If the liquid be transferred to a large glass vessel with cut facets placed in direct sunlight, the effect is very beautiful, flashes of deep gold colored light contrast finely with the rich blue of the liquid.
Case third.—Blue light and red are seen simultaneously and both are diffused.
When sago is made into translucent paste with hot water, it exhibits a distinct bluish color. The paste is to be largely diluted with water and placed in a black vessel, such as a flat gutta percha trough, in which it should form a layer at least an inch in depth. An oblique beam of sunshine passing through a hole of half an inch diameter in the shutter of a dark room, falls upon the surface, forming a bright oval, surrounded by a halo two or three inches in diameter. One half the halo, that farthest from the window, is yellowish red, the other half, bluish.
The proportion of the two colors is nearly equal, and both are equally diffuse. Common starch gives analogous results, not however quite so well marked. And the same effect is produced by milk diluted with about 50 times its bulk of water. With precipitated magnesia I did not perceive the blue light. It was very perceptible with alumina, though not nearly so much so as with milk, which shows the effect remarkably well.
These various effects appear to be all due to one and the same cause, interference. Let us first take the case of the ground glass and consider the effect of a very small abrasion of the surface. At the edge of this abrasion, two parallel impulsions of light pass, the one through the abrasion, the other through the original surface of the glass. At any point beyond, both have traveled the same distance, with this difference that for a very small space corresponding with the depth of the abrasion, the one will have traveled through air while the other will have traveled through glass. The latter ray will have suffered a change of phase corresponding with the retardation occasioned by the glass and proportioned to its index of refraction, and therefore these two rays will be in a condition to interfere with each other.
If we take the index of refraction of the glass at 1.5 it is evident that the ray passing through the natural surface will be retarded in the proportion of 1.5 to 1 for a distance equal to the depth of the abrasion. If this depth be extremely small, the blue rays will interfere, while the less refrangible rays do not. And for different depths of the abrasion we shall obtain a succession of interferences corresponding with the transmitted spectra of Newton's table of the colors of thin plates.
But as these scratches are unequally disposed over the surface and in close contiguity, it is evident that if various colors are produced at every point of the glass, these will re-compose white light, and the transmitted beam will be white. This takes place with common coarsely-ground glass. But if the abrasions are extremely small and very close, an excess of red light will be produced. If they are chiefly but not altogether small, the red light produced by the small ones will be diluted with white light, both that transmitted without interference and that re-composed after interference. And this exactly corresponds with the results observed.
Taking the case of two adjacent waves so striking upon the glass that one passes through the abrasion while the other passes through the glass, let us suppose that the abrasion has a depth of 000475 millimeter, and that the glass has an index of refraction of 1.5; it is evident that a mean blue ray whose wave length in air is .000475 mm. will have accomplished one oscillation while the adjacent wave in passing through the corresponding and equal space of glass will have accomplished exactly one and one half oscillations. Its phase will therefore be precisely the opposite of that of the first wave, and these two will be in condition to extinguish each other by interference. Abrasions therefore of the depth just mentioned will tend to the production of red light by extinguishing a certain portion of the blue.*
The effect of fine particles contained in a film is evidently quite analogous. If one impulse of light passes freely through a collodion film, while the adjacent one encounters and passes through a small particle of oxyd of copper, alumina, etc., it will be retarded or accelerated in comparison with the former according as the index of refraction of the substance is greater or less than that of the pyroyxlin, and in proportion to the relation between the two.
When the red light in place of being direct, is, as in the 3d case, diffuse, it admits of the following explanation. Direct rays of light entering a medium which holds objects of a different refractive power in suspension will be partly transmitted through and between these objects, and partly reflected by
* Although the retardation of glass of 1.5 as compared with air corresponds for a thickness of .000475 mm. with the half wave length of the mean blue ray, it it probable that the most vivid red light would be produced by a somewhat less retardation corresponding with a somewhat less depth of groove or abrasion.
them. As the reflecting surfaces will be irregularly distributed in every direction, the light which is not transmitted will be reflected in every direction. This diffusely reflected light will in some cases pass through the particles, in other cases pass between them. If the particles have a higher index of refraction, those rays that pass through them will be retarded; if a lower index, they will be accelerated. In either case, those that pass through the edges of the particles will be in a condition to interfere with those that pass immediately adjacent. And if the particles be very small, the number of such interferences will be very great, and the preponderance of color produced will be red by the extinction of blue rays.
Nor is this the only way in which interference may take place. If we suppose the two bounding planes of the particles through which the ray passes, to be parallel or nearly so, it is evident that interference may result between the transmitted ray, and another ray twice reflected in the interior of the particle precisely as in the case of the plate of air, etc., in Newton's thin plates.
This latter mode of interference also gives us easily the key to the production of blue diffused color in the second and
For if the bounding planes of the particle be perpendicular then the light irregularly reflected through the liquid falling in some cases with nearly perpendicular incidence upon particles, the ray reflected at the second surface will be in condition to interfere with that reflected at the first; and if the particles be sufficiently small, this will always result in the production of blue light. This interference will take place equally, and the result will be the same whether the particles have a higher or lower index of refraction than that of the medium in which they are suspended.
For, let us in the first place, suppose them to have an index less than that of the medium. The incident ray then suffers reflection at the first surface without change of phase. The transmitted ray is reflected in part at the second surface, the medium having by supposition a higher index of refraction than the particle, a change of phase equal to half an oscillation is produced, and if the particle had no thickness, the two rays would extinguish each other. If we suppose the particle to have an appreciable though small thickness, the blue rays would become concordant with a thickness smaller than that necessary for the red, and the reflected ray will be tinged with blue.
If the particles have a greater index of refraction than the medium, the ray reflected at the first surface will suffer a change of phase, and not that reflected at the second. Thus in either case, whether the particle have a greater or less index than the medium, there will be a difference of phase equal to half an oscillation between the rays reflected at the two surfaces, independently of the thickness of the particle, and this with minute particles will always lead to the production of blue light by the interference of the two reflected beams.
There is one condition that will be particularly favorable for the production of red light by rays both of which pass through the particle and of blue light by rays reflected at the front and back surface: this is when the particles have a spherical form, as will appear from the following considerations.
Let direct rays of light, L, L' strike any sphere S. Those that strike nearly in the direction of a diameter will be principally transmitted. Others striking more obliquely at any point o will be largely refiected. As there are many globules, there will result a
R bundle of rays RRRR, and similar parcels will be irregu
om larly reflected in all angles and directions ; for rays L'OP
Ć will strike at all points of the front hemisphere of the globule S. Let us consider any one set of parallel rays R R R'R. These will strike other spheres and each sphere will receive rays like R' following the course of a diameter. At M a portion of the light will be reflected back and a portion will pass into the sphere, part of which will be again reflected at N. These two last beams returning in the direction MRP will be favorably affected for interfer
In this way, diffuse rays are irregularly reflected in all directions from the surfaces of the spherical globules, and in falling apon other spheres, each direction finds a corresponding diameter bounded by tangential reflecting planes parallel to each other and perpendicular to it. Consequently a much larger proportion of the incident rays are caused to interfere in the case of spherical particles, than of those that are angular or crystallized.
If the spheres be sufficiently small, this will result in the production of blue light returned in some direction MR'. If the spheres be of irregular sizes, the blue light will be more or less diluted with white. These results will follow whether the spheres have a greater or less index of refraction than the medium, for the reason already given.
Another portion of the ray R' passes through the sphere at N and interferes with a ray twice reflected, viz: at N and M, with production of red diffused light in some direction at N P'.
The phenomena which I have endeavored to describe and account for, are not without a certain superficial resemblance as respects their origin, to another set of interference effects produced by fine particles adhering as dust upon mirrors or thick plates of glass. They exhibit this characteristic difference, however, that the colors of thick plates are produced by the interference of two waves diffusely reflected by different particles. Whereas in the phenomena here described, this is not the case.
I have included in this brief description a few only of a very large series of experiments. The conditions may be greatly varied, and many phenomena more or less familiar are ascribable to these causes.
Thus lampblack if extended somewhat thinly over glass by smoking it, gives a film which colors luminous objects viewed through it, deep red, for lampblack in thin films is more or less transparent to light (and also to heat, as shown by Melloni). The same lampblack which thus transmits red light, is capable of diffusing blue, as may be seen, not, indeed by suspending it in water, but by diffusing a small proportion of it through a white pigment. The result is not a mere dilution, which would give gray, but the production of the well marked blue color known as lead-color.
Again, if a jet of steam be thrown out into the atmosphere, it is quickly condensed into fine particles of water. If when the sun is near the horizon, we stand nearly in a line between it and the jet of steam and at thirty or forty feet from the latter, it acquires a strong blue shade.
So when the sun shines through hazy air, its light takes a yellow tinge. The same is the case when it is viewed through à considerable thickness of water, as by a diver. The blue color of the sky, and the red of the morning and evening sky, have been explained in an analogous way. There can be little doubt that the brilliant colors of the clouds at sunset are due to interferences, but in this case the interference is between two waves both reflected, precisely as in the case of halos. An analogous effect to halos can be produced by breathing on a glass plate and observing through it the bright light of the sky as seen through a hole in a dark shutter. This experiment is not new; and the circular form of the interference rings seen depends upon the regularity of the particles. But