Optical tables and data for use of opticians / by Silvanus P. Thompson.
- Silvanus P. Thompson
- Date:
- 1907
Licence: In copyright
Credit: Optical tables and data for use of opticians / by Silvanus P. Thompson. Source: Wellcome Collection.
101/148 page 89
![under the heading D, or /xD. Also the medium dispersion is given, that is to say the difference between /x0, the refractive index for red light of the quality of the “ C ’’-line, and /xF, the refractive index for blue-green light of the “ F ’’-line of the spectrum. This is written /xF—/x0 or for brevity A/x, meaning the difference between the /x’s. Now if this dispersion were always propor¬ tional to the mean refraction uD — 1, the fraction —- or — /A —- would be the same for all glasses. A/x A glance at the last column of any of the Tables of Re¬ fractive Indices will show at once that so far from this being the case the numbers vary widely. This ratio is all-important in the practical calculation of lenses; it states the amount of refraction for a given amount of dispersion, and is often denoted by the symbol v. We see that in the lightest kind of pure glass, Table [16], v is worth 70, while in the heaviest (flint) kind it is worth 19*7. The values of v in Chance’s glasses range from 64- 6 to 29 • 9. Now it is obvious, on a little thought, that if we want to so combine two lenses that they shall neutralise one another’s dispersion, two conditions must be fulfilled:—(a) the lenses must be of opposite kinds, one + the other — ; (6) their refracting powers must be so chosen that the refracting lens of greater refracting power shall produce exactly as much dis¬ persion as the lens of lesser refracting power. This last pro¬ vision clearly implies that the respective powers of the two lenses chosen shall be proportional to their respective values for v. Understanding this, nothing is easier than to make an achro¬ matic lens. For example, in Chance’s list of glasses there is a “hard crown” for which v is 60'5, and an “extra dense flint,” for which v is 29 • 9. The crown gives almost exactly twice as much refraction for an equal dispersion as com¬ pared with the flint. Hence, if we take a + lens made of this crown, of a power proportional to 60*5, and a — lens made of this flint of a power proportional to 29 • 9, they will have equal and opposite dispersions. Let us then take a plano-convex crown of + 6-05D and a plano-concave flint of — 2’99D, and cement them back to back like Pig. 45. They will make an achromatic lens of a power of -f 3-04D. Again, in Chance’s list there is a “ dense flint,” for which v = 36. If we were to](https://iiif.wellcomecollection.org/image/b28064732_0101.jp2/full/800%2C/0/default.jpg)
