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rays, lenses, called, convex, aberration, light and focal

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LENS, a transparent body, generally glass, which refracts the rays of light convergently or divergently. Converging lenses, properly speak ing, are called positive (trade designation plus, +), because they bring rays of light to an actual focus, forming a real image. Con verging lenses give, under suitable conditions, a magnified image of an object, and one or both of their bounding polished surfaces are convex. The fact of their being thicker in the middle than at the edges distinguishes them from diverging lenses. Diverging lenses are called negative (trade designation, minus, —) because they tend to cause the rays of light to diverge and form, under 411 conditions, a virtual, reduced image of an object. One or both of their surfaces are concave and they can be dis tinguished from converging lenses by their be ing thinner in the middle than at the edges. These two classes of lenses are each divided into three leading types. Those of the positive or convex class are (I) double or biconvex; (II) plano-convex; (III) convex-meniscus (trade term, periscopic-convex). Those of the negative or concave class are (IV) double or hi-concave; (V) plano-concave; (VI) concave meniscus (trade term, periscopic-concave). (See Fig. 1). Convex lenses converge parallel rays, as shown in Fig. 2, to a point (c) called the principal focus or focalpoint, and the dis tance from a certain point (b), called a prin cipal point, which is usually within the lens, to the focal point (c) is the equivalent focal length. The straight line (d b c) which passes through the middle of the lens, joining the centres of the curvature of the two surfaces, is called the principal axis.

For brevity, the word ((focus° is often used instead of focal length. In a concave lens, the action on parallel rays is opposite to that of a convex lens; instead of converging the light, it diverges the rays away from the axis, as shown in Fig. 3. The imaginary extension of the di verging rays should meet at c, and when, as in the case of the convex lens, the incident rays are parallel, the distance from the virtual focus c to the principal point b is the equivalent focal length. It will be noticed from the diagrams that the rays of light entering the substance of the lens are always bent toward the thickest part of the lens. Generally speaking, the real

called cylindrical lenses, or cylinders. In these lenses a line drawn along the summit of ture, parallel to the axis of the imaginary cylin or virtual focus increases with the increase of radius of curvature of the polished surfaces. The power of any lens is the quotient obtained by dividing unity by the equivalent focal length. A lens is said to be neutralized when combined with one of equal and opposite power, giving the effect of a plane glass. The distinctness of the image formed by a simple lens depends mostly on the extent to which the spherical aberration and the chromatic aberration are present, the aberrations being greater as the ratio of diameter to focal length increases in a lens of any given type. Spherical aberration of a lens is caused by the rays meeting at different intervals along the axis instead of combining at one point. In Fig. 4, of is the spherical aberra tion. Chromatic aberration is due to the sepa ration of the light into its different colors, thus causing, in the case of a convex lens, the violet rays to meet at a point v nearer is lens than do the red rays at point r. In Fig. 5 vr s the chromatic aberration. Both of these defects are corrected in achromatic lenses. The process by which this is accomplished is the combining of two or more lens forms of different kinds of glass which have differing angles of re fraction. These are accurately fitted together and cemented into one piece. A very common combination is a convex crown glass with a der, is called the axis, and must be distinguished from the principal axis of a spherical lens. (Fig. 6). When the lens has two cylindrical sur faces, with the axes at right angles, it is called a °crossed if one of the surfaces is spherical and the other cylindrical, the lens is called a asphero-cylinder.)) Another form of lens which has come into use in recent years is the toric (toroidal) lens on which one surface is toroidal, the meridians of the surface are at right angles to each other and have radii of concave flint glass. A still better combination is a central disc of flint glass with a crown disc on each side of it — all being optically ground so as to correct both chromatic and spherical aberration.

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