62.—Spherical Aberration.—If the surfaces of convex lenses are truly spherical, it is found, by an analysis too complex to be described in this work, that the rays which pass through at different distances from the axis converge to slightly different points of distance. This subject was at one time seriously discussed for the proper formation of objectives for telescopes; but at present it is entirely neglected by the optician, as it is found practically to be as difficult to make a lens truly spherical as one of the convergent or divergent form required under the special conditions present. The spherical form, as it is approximately produced from the grinding with spherical tools, being always nearly correct, the correct forms of object-glasses are made by figuring, which has been already referred to, art. 38. In eye-pieces the spherical aberration would cause some confusion were the glasses not adjusted in such a manner as largely to prevent this.
63.—The Formation of Images by Refraction from a Convex Lens.—If we take any double convex lens, as that shown in section Fig. 6, we find, if it is held towards the sun at a certain distance from a solid surface, we form a burning-glass,—that is, we produce an image of the sun where his rays of light and heat are refracted by the whole of the surfaces of the glass. The distance from the centre of the lens to the point of greatest light is called the solar focus of the lens,—that is, the point at which it concentrates or converges parallel rays, and forms the image of the sun. With parallel rays from the sun, the distance of focus is less than if these rays were divergent in any degree. Consequently the solar focus is less than that subtended by any object on the earth.
Fig. 8.—Diagram of the convergence of rays of light.
Larger image
64.—In the diagram, Fig. 8, a candle-flame at acb forms its focus at a‴c‴b‴, where all rays converge to form an image in the following manner:—Every point of the candle throws its light upon every point of the surface of the lens, and, therefore, throws the image of each point to its focal position behind the lens, according to the direction of its refractions; so that, if we take all the separate points of light thrown from the candle, we then have a perfect image of it formed by an infinite number of separate focal points, and as the rays by their direction necessarily cross over the axis the image is in an inverted position.
65.—The whole of these lines would form a confusion if shown in a diagram. We may, therefore, take for illustration the exterior of a cone of rays proceeding from three points only. Thus the clear lines aa′ and aa″ from the point of the flame would refract to the lower part of the image a‴. The dotted lines bb′ would proceed to the upper part of the image, as shown by the continuation of the dotted lines to b‴, whereas the central dash lines c′c″ would form their images in the centre following the dash lines to c‴, and thus, from the number of luminous points, the whole image of the candle would be produced at the foci b‴c‴a‴ in an inverted position.
66.—Dispersion of Light.—The conditions stated above for refraction of monochromatic light would not answer for perfect vision, which is only possible in clear white light. It therefore becomes necessary in practice to correct the quality of dispersion which light suffers in refraction through any dense medium. The evidence of dispersion by glass may be shown by a prism, as in the following diagram:—
Fig. 9.—Diagram showing chromatism of light by the prism.