LEMONS, SALT OF, a name improperly applied by druggists to binoxalate of potash. [OXALIC Am.] LENS (Latin for " a small bean "), a name given to a glass, or other transparent medinm, ground with two spherical surfaces in such manner as to be generated by the revolution of one or other of the following figures about the axis A B.
(1) is plano-convex ; (2) is double-convex ; when the radii are equal it is called equi-convex, and when one radius is 6 times the other it is called a crossed lens; (3) is a meniscus ; in every such lens the concave side has the larger radius ; (4) is plano-concave ; (5) is double concave; (6) is concavo-eonvex.
We shall not here enter upon the laws of optics, but presuming them known, shall collect the principal facts and formula connected with the passage of a direct pencil of light, that is, of a pencil whose rays are either parallel to the axis, or converge to or diverge from a point in the axis. We shall follow the notation (for the most part) and formulte of Mr. Coddington, in his standard work entitled A Treatise on the lieflexion and Refraction of Light,' Cambridge, 1829, which contains a most complete investigation of the subject ; referring to the work itself for demonstration and extension.
The following figure represents the passage of a pencil of light with parallel rays through a double-convex lens. The rays are not all re fracted to a point, but are tangents to a CAUSTIC, which has a cusp at a certain point F, and may be considered with sufficient accuracy as a small portion of a semicubical parabola. If however the aperture of the lens be no considerable portion of a sphere, which is always the case in practice, the rays which pass near the axis are thrown so thick about the point F, that the effect is an image of the extremely distant point from which the rays come, formed at F. This (for parallel rays) is called the focus of the glass, and its distance from the nearest side of the lens is called the focal distance. The longitudinal aberration of a ray is the distance from the focus at which it passes through the axis, and the latitudinal aberration is the perpendicular distance from the axis at which it passes through a perpendicular drawn through the focus. Thus, in the following figure, F A is tho longitudinal, and F the latitudinal aberration of the ray P q.
We shall first state the method of finding the focal length of a given lens. Let iz be the index of refraction, or : 1 the constant propor tion which the sine of the angle of incidence bears to that of refraction (which for plate-glass varies from to ; for crown-glass, from to 1.563; and for flint-glass from 1.576 to P642); and let n and s be the radii of the two sides of the lens with their signs, while r and s are the numerical values of these radii independently of their signs. Also let every convex surface be considered as having a positive radius, and every concave surface a negative ono. Let F be tho focal distance with its sign, and f the numerical value of the same, it being agreed that the focal distanco shall be positive when parallel rays are made to converge, and negative when they are made to diverge, that is, to proceed as if they came from a point on the same side of the glass as that ou which they entered. One formula, upon these suppositions, will embrace all the cases ; and that formula is 1 _ I 1) = 44— 1) (— R on the supposition that the central thickness of the lens is inconsider able. But if this thickness, though small, be large enough to render it necessary to take it into account, let the thickness be called t, and let R be the radius of the side at which the light enters : then either find F from • F being found from the preceding : the result is sufficiently correct.
The focal distance, as determined from the first formula, is the same whether the light enter on one side or the other, but the correction for the thickness depends, as we see, upon the 'side at which it enters.
The application of these formula to the several cases is as follows : We write the distinctive adjective of the lens so that the first part of the word shall denote the part at which light first enters ; for instance, plano-convex, or convexo-plane, according as the light first meets the plane or convex surface.
In all the preceding cases r is positive ; or all sharp-edged lenses make parallel rays converge : but in those which follow it will be noted that F is negative, or all flat-edged lenses make parallel rays diverge.