Page:The American Cyclopædia (1879) Volume XII.djvu/673

OPTICS 659 and with spherical surfaces. As with mirrors, so with lenses, by considering any curved sur- face as composed of a multitude of minute plane surfaces, we at once extend to them the law of refraction ; and it is then only necessary to know the angles of incidence and the value ivr FIG. 13. of c, in order to trace the course of the rays. The refraction toward a perpendicular at the first surface of a lens will conspire with that from the perpendicular at the second surface, both occurring in the same actual direction in space. A ray passing through the centres of curvature, and F, fig. 13, of the surfaces, passes also through the middle point of the lens, and is not refracted. This line M F is the axis of the lens. Kays parallel to this axis are, when the lens is convex, brought to meet in a real focus F lying at some point in the axis ; they are made to diverge as from a virtual focus somewhere in this line, whenever the lens is concave. The aperture of a lens is the total arc or number of degrees of curvature of sur- face on the two sides of the axis through which light is allowed to pass. Hence, it does not depend on size alone ; and the minute lens which is merely a bead of glass has almost necessarily a much greater aperture than a lens of some inches or feet focus. The principal focus F of a double convex or double concave lens, of crown glass, of equal curvatures, is at the centre F of the sphere of which the lens surface END forms part ; the focal distance is equal to radius; for the plano-convex and plano-concave, it is equal to twice the radius. The general rule for finding the focal distance is : For the meniscus and concavo-convex lens, divide twice the product of the radii of curva- FIG. 14. ture by their difference ; for the double convex and concave, by their sum. When, for the double convex lens, the object is at any dis- tance greater than twice the radius, on one side, the image is always somewhere between the focus and the other side of the sphere or the distance of twice the radius, on the other ; and here, again, the places of object and image are interchangeable ; the foci are conjugate. Fig. 14 shows the manner in which the image I of the candle is formed by the lens L S. Cones of rays, having for their basis the surface of the lens and for their apices every point on the surface of the candle facing the lens, are refracted by the lens to points in the image corresponding to the points in the candle from which the rays emanated. When the object is brought within the princi- pal focus on either side, the image is then on the same side, or virtual, erect, beyond the fo- cal distance, and magnified. So, in the former case, the real image is magnified by bringing the object nearer the focus. The simple act of bringing an object at less than the ordinary distance of distinct vision from the eye, as when we look at small objects close to the eye through a pin hole, increases the visual angle, and so proportionally magnifies them. Hence it is that, for objects viewed as placed within the principal focus, the magnifying power in- creases with diminution of focal distance of the lens, being determined conveniently by the quotient of the ordinary limit of vision, say 8 inches, divided by the focal distance of the lens. Thus a lens, focal distance -fa of an inch, has a linear magnifying power of 8-5-^=400 times; and of course a superficial magnifying power of 400 2 =160,000 times. Thus are ex- plained the very high powers obtained by the use of minute spherical lenses in form of beads, of perfect glass. But it is only for a small aperture, say 6 or at most 8, that the rays are brought rigidly to one focus. Enlarging the aperture, the successive rings lying with- out bring their light to foci successively nearer the lens ; passing their foci, these rays diverge, and form an indistinct border of light about the image. This is spherical aberration of lenses. It is to some extent corrected by pe- culiar forms of lens, hence called aplanatic ; the least spherical aberration thus obtained is with a double convex lens, the radii of whose curvatures are as 1 : 6 ; this, with the surface whose radius is 1 toward the object, gives an aberration of TOT times its own thickness. III. DISPERSION. The dispersion of light is the separation of the colors existing, actually or potentially, in white or solar light. It may occur by refraction, by diffraction, or by inter- ference. (See COLOR.) The total length of spectrum obtained by prisms, i. e., the total dispersion, and also the amount of spreading out of the different colors, differ with the na- ture of the medium or prism employed. Call- ing the refrangibility of the violet ray V, and of the red R', for a given prism, and the coef- ficient of refraction c, the dispersive power is = Y/ "^'. This ratio, for oil of cassia, is '139 ; for flint glass, "052 ; Canada balsam, -045 ; dia- mond, -038 ; crown glass, '036 ; water, -035 ; rock crystal, '026. Thus, for example, the to-