185 



LEMONS, ACID OF. 



LENS. 



188 



LEMONS, ACID OF. [CITRIC ACID ] 



LEMONS, ESSENTIAL OIL OF. This well-known essence is 

 extracted from the little cells visible on the rind of lemons, by submit- 

 ting raspings of the fruit to pressure. It may also be obtained by 

 distilling the peel with water, but the product is less agreeable 

 although not so liable to undergo decomposition, owing to the absence 

 of mucilaginous matter. 



When pure, essential oil of lemons is colourless and limpid ; specific 

 gravity 0'847 at 70 Fahr. ; boiling point about 145 Fahr. ; soluble in 

 all proportions in alcohol or ether. It is nearly all composed of a 

 hydrocarbon, isomeric with oil of turpentine, CITREN or Citronyl, the 

 boiling point of which is 329 Fahr., and specific gravity 0'S57. An 

 oxidised portion is also present, the composition of which has not been 

 determined. 



The greater portion of commercial oil of lemons is imported from 

 Portugal and Italy, some however from France. It is very frequently 

 adulterated with oil of turpentine. 



LEMONS, SALT OF, a name improperly applied by druggists to 

 binoxalate of potash. [OXALIC ACID.] 



LENS (Latin for " a small bean "), a name given to a glass, or other 

 transparent medium, grosnd 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 



(1) is plano-convex ; (2) ig 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-convex. 



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 formuhc 

 <>f Mr. Coddington, in his standard work entitled ' A Treatise on the 

 Keflexion 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 r, 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 r, 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 [>erpendicular distance from 

 the axis at which it passes through a perpendicular drawn through the 

 focus. Thus, in the following figure, F A is the longitudinal, and K B 

 the latitudinal aberration of the ray P Q. 



We shall first xtate the method of finding the focal length of a given 

 Let n bo the index of refraction, or M : 1 the constant propor- 

 tion which the sine of the angle of incidence bears to that of refraction 

 (which for plate-glass varies from I'oOO to 1'540 ; for crown-glass, from 

 l-.V-'S to 1-663; and for flint-glass from 1'576 to 1'642); and let B and 

 s be the radii of the two sides of the lens with their fiynt, while r and g 

 arc 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 one. Let F be the focal distance 

 with its sign, and / the numerical value of the same, it being agreed 

 that the focal distance hall 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 on which they entered. One formula, upon these suppositions, 

 will embrace all the cases ; and that formula is 



} -:<-->> (k * * 



on the supposition that the central thickness of the lens is inconsider- 

 able. But if this thickness, though small, be large enough to reader it 

 necessary to take it into account, let the thickness be called t, and let 

 H be the radius of the side at which the light enters : then either find 

 F from 



1 , .. 1 l\ (."-I)- t 



or correct F, as found from the preceding formula, by subtracting from 

 its algebraical value 



n B' 



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. 



(1). Plano-convex : n is infinite, s=s. 



(1). Convexo-plane: R = r, and s is infinite : 



_! ft 1 (M l)-_t r t_* 



F B jUK'- ' * ~ JU 1 ~~ Ji' 



(2). Double-convex : B = ) - ,s=s: 



(3). C'jKKJd-concave meniscus: R = )', s = s, r<s; 



^ = (/-!) (;- 



(3). Conraro-conw.r meniicut : n= ; 

 1 



S = s, !> : 

 '-!)' 



> ^ = /' 



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. 



(4). Plano-concave : n is infinite, s = s : 



(4). Concavo-plane : B = r, 8 is infinite : 

 1 i 



(5). DoMe-concarc : u 

 1 



1 

 7 



(6). Convexo-concarc : 



(6). Concavo-convex : B = 



F=(> 

 1 



* These 



