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67.—In Fig. 9 let P represent the section of a prism of glass, covered except at the narrow opening a. Let a strong light, as shown, be covered, except from a narrow slit, then the ray from the light, refracted from a towards a′ in the prism, will be dispersed or split up at a into the colours of the rainbow, shading from blue, green, and yellow, to red, within the prism. Upon emergent refraction at a′ this dispersion will increase so that an image of the slot near the light, if thrown on a plane proceeding from the base of the prism to the right, will be represented at BGR by a prismatic or chromatic spectrum, as it is termed, shading off from blue to green, yellow, red.
68.—Achromatism of the Prism in the same Quality of Glass.—Taking the prism, Fig. 10, C as before, and applying a second exactly similar prism C′ reversed upon the face of the first—then at every part of the process of dispersion from a point of white light under diffraction into the first prism, will by equal diffraction, in passing through the second prism, be brought to a point, where it will issue a white ray at the point a″, as it entered at the point a; or, practically, the emergent ray will be achromatised. This principle must be followed in the manufacture of achromatic lenses, although under various indices of refraction and dispersion from differences in qualities of glasses. It is made use of in the achromatism of eye-pieces, and in combinations, and assures the achromatism of parallel glasses used for sextants under different angles of incidence.
Fig. 10.—Diagram perfect achromatism.
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69.—The Achromatic Lens.—The achromatism of a pair of lenses by which a large amount of refraction of pure white light is obtained, depends upon differences in the qualities of glasses which are due to their density and chemical composition, so that in one glass a less amount of dispersion is produced at an angle which gives an equal amount of refraction than in another. The combinations of glasses in use are crown and flint, as already described, [art. 32], the crown being a light glass of soda and silica, the flint being a heavier glass containing silica, potash, and lead. In a certain kind of flint glass used for optical purposes, for a prism giving only slightly greater refraction than one of crown glass, the dispersion is about double. Therefore, we may combine a pair of glasses so as to obtain a desired amount of refraction from the combination if we make the crown glass refract something over double the amount we require for the perfected lens or prism, and diminish this quantity by the reverse refraction of the flint glass, thereby correcting the dispersion, as may be shown by the diagram on this page.
70.—In fig. 11 let C be a prism of crown glass giving over double the amount of refraction to a prism of flint glass F, but only of total dispersion equal to the thicker crown glass. The compound white ray of light a will then be dispersed upon refraction at the meeting faces of the two prisms, a certain quantity represented by the cone of rays shown, and again converge at a′, an equal quantity on emergence from the exterior surface of the flint prism, so as to issue again a white ray, of which this system of prisms has refracted, but not dispersed, the light.
Fig. 11.—Showing principles of achromatism.