Dispersion (optics)

“ Finally, when the vibration-direction corresponding to the refractive index β, or the “third mean line,” has a fixed position, the optic axial plane lies in the plane (010) , but the acute bisectrix may vary in position in this plane; the interference figure will then be symmetrical only about a line joining the optic axes (“inclined dispersion”) . Examples of substances exhibiting these three kinds of dispersion are borax, orthoclase and gypsum respectively. ”

“ The difference of the angles of deviation for two selected rays measures their dispersion, and if this angle is divided by the deviation of the mean ray, we obtain the dispersive power of the prism. Transparent media vary in their dispersive powers; for example, carbon disulphide has more than three times the dispersive power of crown glass. The true nature of dispersion was first demonstrated by Newton, who concluded that the colours of the spectrum were homogeneous and caused by simple vibrations of definite wave-length, the different colours being unequally refrangible. ”

“ The simplest way of showing dispersion is to refract a narrow beam of sunlight through a prism of glass or prismatic vessel containing water or other clear liquid. As the light is twice refracted, the dispersion is increased, and the rays, after transmission through the prism, form a divergent system, which may be allowed to fall on a sheet of white paper, forming the well-known solar spectrum. ”

“ On the other hand, while in the older crown and flint glasses the relation between refraction and dispersion had been practically fixed, dispersion and refraction increasing regularly with the density of the glass, in some of the new glasses introduced by Abbe and Schott this relation is altered and a relatively low refractive index is accompanied by a relatively high dispersion, while in others a high refractive index is associated with low dispersive power. ”

“ When the map is not normal, the dispersion of course varies in different parts. It increases rapidly toward the violet end when the spectrum is formed by a prism. Accordingly, in this case the dispersion given will be that of the point whose wave length is 400. ”

“ The dispersion of light is estimated by the variable angle formed by the red and violet rays which bound the solar spectrum;—or rather, it is the excess of the refraction of the most refrangible ray above that of the least refrangible ray. The dispersion is not proportional to the refraction—that is, the substances which have an equal mean refraction, do not disperse light in the same ratio. ”

“ THE discovery that the laws of refractive dispersion of different substances were such as to allow of combinations which neutralised the dispersion without neutralizing the refraction, is one which has hitherto been of more value to art than to science. The property has no definite bearing, which has yet been satisfactorily explained, upon the theory of light; but it is of the greatest importance in its application to the construction of telescopes ”

“ Irrationality of Dispersion.—If we compare the spectrum produced by refraction in a glass prism with that of a diffraction grating, we find not only that the order of colours is reversed, but also that the same colours do not occupy corresponding lengths on the two spectra, the blue and violet being much more extended in the refraction spectrum. The refraction spectra for different media also differ amongst themselves. This shows that the connexion between the refrangibility of light and its wave-length does not obey any simple law, but depends on the nature of the refracting medium. ”

“ If the refractive powers of the lenses were exactly proportional to their dispersive powers, as Newton erroneously thought, it is evident that the concave lens would pitch all the rays outwards to an amount which would annul both the chromatic variation and the total refraction of the convex lens, leaving the pair without power to bring anything to a focus. Fortunately flint glass as compared with crown glass has nearly double the dispersion between red and violet, and only about 20% greater refractive power for the intermediate yellow ray. ”

“ The whole spectrum of the moving object, in fact, is very slightly shoved hither or thither, according as it is travelling towards or from the eye; but, for convenience of measurement, one line is usually picked out from the rest, and attention concentrated upon it. The application of this method to the stars, however, is encompassed with difficulties. It needs a powerfully dispersive spectroscope to show line-displacements of the minute order in question; and powerful dispersion involves a strictly proportionate enfeeblement of light. ”

“ According to the wave-theory of light, refraction (q.v.) is due to a change of velocity when light passes from one medium to another. The phenomenon of dispersion shows that in dispersive media the velocity is different for lights of different wave-lengths. In free space, light of all wave-lengths is propagated with the same velocity, as is shown by the fact that stars, when occulted by the moon or planets, preserve their white colour up to the last moment of disappearance, which would not be the case if one colour reached the eye later than another. ”

“ A sunbeam received on a screen, after passing through a small round hole in a window-shutter, appears like a round white spot; but when a prism is interposed, the beam no longer occupies the same space. It is separated into the prismatic colours, and spread over a line of considerable length, while its breadth remains the same with that of the white spot. The act of spreading or separation is called the dispersion of the coloured rays. Dispersion always takes place in the plane of refraction, and is greater as the angle of incidence is greater. ”

“ So by means of a lens of a certain substance of low dispersive power we can form an image slightly coloured, and we can add another lens of a substance having a high dispersive power and less curvature and just reverse the dispersion of the first lens without reversing all its deviating power. ”

“ But for anyone who bears in mind the great results of the atomic theory of dispersion and who does not renounce the simple explanation which this theory gives for the dependence of the refractive index upon the color, without introducing something else in its place, the idea that a moving absolutely transparent medium, whose refractive index is absolutely , shall yet have a notable influence upon the velocity of propagation of light, as the theory of Cohn demands, is not possible of assumption. ”

“ It should be observed that at the surface of bodies the refractive power is exerted, and that the light proceeds in a straight line until leaving the body. The refraction is more or less, and in all cases in proportion as the rays fall more or less obliquely on the refracting surface. It is this law of optics which has given rise to the lenses in our camera tubes, by which means we are enabled to secure a well-delineated representation of any object we choose to picture. ”

“ Fig. 143.—Simple Objective Prism.
When one comes to solar spectroscopy one meets an entirely different situation. In stellar work the difficulty is to get enough light, and the tendency is toward large objectives of relatively short focal length and spectroscopes of moderate dispersion. In solar studies there is ample light, and the main thing is to get an image big enough to be scrutinized in detail with very great dispersion. ”

“ One-twentieth to one-fiftieth of an inch is suitable. The aperture and the number of bands being both fixed, the condition of blackness determines the angular magnitude of a band and of the spectrum. The use of a grating is very convenient, for not only are there several spectra in view at the same time, but the dispersion can be varied continuously by sloping the grating. ”

“ This is due to no other cause than that which produces [Pg 112] the rainbow and the spectrum—the separation, or "dispersion" in their passage through a refracting medium, of the variously coloured rays composing a beam of white light. In an ordinary lens there is no common point of concentration; each colour has its own separate focus; and the resulting image, formed by the superposition of as many images as there are hues in the spectrum, is indefinitely terminated with a tinted border, eminently baffling to exactness of observation. ”

“ The whole subject of the colors of objects, both opake and transparent, is still in obscurity. Newton’s conjectures concerning the causes of the colors of natural bodies, appear to help us little; and his opinions on that subject are to be separated altogether from the important step which he made in optical science, by the establishment of the true doctrine of refractive dispersion. ”

“ The spectra produced by different dispersive media not only differ in length, but also in the breadth of the coloured spaces not being in the same ratio to each other; hence the spectra are said to be irrational, or the dispersion is said to be irrational.
Vision.—The visibility of an object depends upon the rays of light which emanate from each point of its surface presented to the eye being brought to a focus upon the ret ́ina or expansion of the nerve of sight lining the inside of the back of the eye ”

“ But inasmuch as the telescope or line of vision is inclined at the angle of dispersion to the direction of the incident ray, ordinary aberration must come in, as it always does when an observer moves athwart his line of vision; and so there will be a spurious or apparent Doppler effect due to common aberration. That is to say a spectrum line will not be seen in its true place, but will appear to be shifted by an amount almost exactly imitative of a real Doppler effect—the imitation being correct up to the second order of aberration magnitude. ”

“ This conventional equation simply states that the sum of the reciprocals of the radii of the crown lens multiplied by the dispersion of the crown, must equal the corresponding quantity for the flint lens if the two total dispersions are to annul each other, leaving the combination achromatic. Whatever glass is used the power of a lens made of it is
P ( = 1/f) = Σρ (n - 1)
so that it will be seen that, other things being equal, a glass of high index of refraction tends to give moderate curves in an objective. ”

“ It will readily be conceived that the unequal refrangibility of light must give rise to a good deal of confusion in all images produced by refraction. For instance, a pencil of rays diverging from a point on the axis of a convex-lens will be collected, not to one single focus, but to a series of foci lying at different distances from the lens along its axis, and there will consequently be a confusion analogous to that arising from the aberration which we found to be produced by the spherical form of a refracting surface. ”

“ If we now suppose half the grating cut away, so as to leave 1000 lines in half an inch, the dispersion will not be altered, while the brightness and resolving power are halved.
There is clearly no theoretical limit to the resolving power of gratings, even in spectra of given order. But it is possible that, as suggested by Rowland, [2] the structure of natural spectra may be too coarse to give opportunity for resolving powers much higher than those now in use. ”

“ For, first, when the correcting lens is approximately constructed on a calculation founded on its intended aperture, and on the refractive and dispersive indices of its materials, the final and complete dispersion of colour may be effected, not by altering the lenses by grinding them anew, but by shifting the combination nearer to, or farther from, the object-glass, as occasion may require, along the tube of a telescope, by a screw motion, till the condition of achromaticity is satisfied in the best manner possible. ”

“ The image of this zone upon the screen is crossed by portions of the iris-rings. Subjecting the reflected beam to prismatic analysis, the resultant spectrum may be regarded as an indefinite number of images of the zone placed side by side. In the image before dispersion we have iris-rings, the extinction of the light being nowhere complete; but when the different colours are separated by dispersion, each colour is crossed transversely by its own system of dark interference bands, which become gradually closer with the increasing refrangibility of the light. ”

“ THE phenomena of refraction and dispersion teach us that a body in a state of intensest heat emits not alone powerful thermal rays, but also all possible sorts of light (luminous colors) . Diffraction convinces us that radiation is a wave-motion of an extremely fine, elastic, fluid medium, ether, and at the same time it enables us to compute the wave-length of the single rays. ”

“ Luminous undulations ought to produce a similar effect when the medium in which they are excited is terminated by a body in which the density of the ethereal fluid is different; that is to say, there must be produced a reflected wave and one transmitted; which is, in fact, what we call reflexion and refraction. In this system, the intensities of rays of light must be measured by the vis viva of the fluid in motion, that is, by the product of the density of the fluid by the square of the proper velocity of its particles. ”

“ Let us suppose that we are looking at a coloured object—let us say, a red railway signal-lamp; from the lamp to our eye there flows a continuous line of luminous undulations; these undulations enter the eye and become depicted on the retina. For every wave that passes through the pupil, there is a separate and corresponding vibration of the optic nerve, and the number of these vibrations that take place in the course of a second can be easily calculated if we know the velocity of light and the breadth of the waves. We have before found that light travels at the rate of 185,000 miles per second ”