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.
The further they depart from the ratio of refractive index to dispersive power found in the older glasses, the greater the difficulty found in obtaining them of either sufficient purity or stability to be of practical use.
- The optical desideratum is uniformity of refractive index and dispersive power throughout the mass of the glass.
The symbol v represents the inverse of the dispersive power, its value being (nD-i)/(C-F).
The spectrum will be straight if the twoprismsaresimilar in dispersive property, but if one of them is con structed of a material which possesses any peculiarity in this respect it will be revealed by the curvature of the spectrum.
The phenomenon of dispersion shows that in dispersive media the velocity is different for lights of different wave-lengths.
The dispersive powers of gases are, however, generally comparable with those of liquids and solids.
If the refracting angleof the prism is small, then the ratio of the dispersion to the mean deviation of the two rays is the dispersive power of the material of the prism.
If we denote its deviation by S D, then we may put Dispersive power = (F - Sc)/S D.
The second of these two expressions is generally given as the definition of dispersive power.
Glasses can now be made differing considerably both in refractivity and dispersive power.
The irrationality of dispersion is well illustrated by C.Christiansen's experiments on the dispersive properties of white powders.
These effects are due to the difference in dispersive power of the powder and the liquid.
Thus the ether within the dispersive medium is loaded with molecules which are forced to perform oscillations of the same period as that of the transmitted wave.
Opticians should supply sufficient information of the dispersive properties of their materials to allow dµ/dX to be calculated easily for different parts of the spectrum.
Kundt,' who initiated this line of investigation, came to the conclusion that the absorption spectra of certain organic substances like cyanin and fuchsin were displaced towards the red by the solvent, and that the displacement was the greater the greater the dispersive power of the solvent.
This law cannot be maintained in its generality, but nevertheless highly dispersive substances like carbon bisulphide are always found to produce a greater shift than liquids of smaller dispersion like water and alcohol.
The primary reason for this retention is that nothing approaching the difference in dispersive power between ordinary crown glass and ordinary dense flint glass (a difference of i to 13) has yet been obtained between any pair of the newer glasses.
The figures given are the partial dispersions for ordinary crown and ordinary extra dense flint glasses, styled in Messrs Schott's catalogue of optical glasses as o 60 and 0.102 respectively, having refractive indices of 1 5179 and 1.6489 for the D ray respectively, and (µ D -I)/(l F -µc) =60 2 and 33.8 respectively to indicate their dispersive powers (inverted), = v.
This case well illustrates the much closer approach to strict rationality of dispersion which is obtainable by using two different sorts of glass for the two positive lenses, even when one of them has a higher dispersive power than the glass used for the negative lens.
If there be refraction at a collective spherical surface, or through a thin positive lens, 0' 2 will lie in front of O' 1 so long as the angle u2 is greater than u 1 (" under correction "); and conversely with a dispersive surface or lenses (" over correction ").
If the refractive index for one colour be n, and for another and the powers, or reciprocals of the focal lengths, be 4) and 4)+4, then (I) dï¿½/ 4) = dn/ (n - I) =1 /v; do is called the dispersion, and v the dispersive power of the glass.
Therefore 4) 1 and 42 must have different algebraic signs, or the system must be composed of a collective and a dispersive lens.
Consequently the powers of the two must be different (in order that 4) be not zero (equation 2)), and the dispersive powers must also be different (according to 4).
Newton failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors.
Of crown glass and a dispersive lens II.
Of flint glass must be chosen; the latter, although the weaker, corrects the other chromatically by its greater dispersive power.
For an achromatic dispersive lens the converse must be adopted.
To the greater power belongs the weaker dispersive power (greater v), that is to say, crown glass; consequently the crown glass must have the greater refractive index for astigmatic and plane images.
In all earlier kinds of glass, however, the dispersive power increased with the refractive index; that is, v decreased as n increased; but some of the Jena glasses by E.
If its chromatic effect (d4/4) be greater than that of the same lens, this being made of the more dispersive of the two glasses employed, it is termed " hyper-chromatic."
In this primitive Pneuma there must reside the utmost tension and heat; for it is a fact of observation that most bodies expand when heated, whence we infer that there is a pressure in heat, an expansive and dispersive tendency.
In consequence of its low refractive and dispersive power, colourless pellucid fluor-spar is valuable in the construction of apochromatic lenses, but this variety is rare.
Differences of refractive index produce their greatest dispersive effects when incidence on the refracting surface is nearly tangential.
It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive indices; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances.
On the whole, there is probably no treatise so masterly as Aristotle's Ethics, and containing so much close and valid thought, that yet leaves on the reader's mind so strong Transi= an impression of dispersive and incomplete work.
Lord Rayleigh has pointed out that all theories are defective in that they disregard the fact that one at least of the media is dispersive, and that it is probable that finite reflection would result at the interface of media of different dispersive powers, even in the case of waves for which the refractive indices are absolutely the same.
By introducing a dispersive lens of flint the magnifying glass could be corrected for both chromatic and spherical aberrations.
To an achromatic collective lens, which is turned towards the object, a dispersive lens is combined (this type to a certain extent belongs to the compound microscope).
By altering the distance of the collective and dispersive members the magnification can be widely varied.
In the case of the dispersive eyepiece, on the contrary, no sharply limited field can arise, but vignetting must occur.
This gives at once Dispersive power= F - µc)/(y D - I).