TELESCOPE. 



of as much importance ai magnifying power ; and it will / _!_^ vvhen the rays fall diverging on the faid lens. 



be feen hereafter, that there is a certain d.ftance between y - J - r) 

 the Icnfcs that promotes this quality the moll poflible, 

 whatever be the radii of the two lenfes. This condition is 



wnaievcr oe iiic lauu ui mv .."« --- 



fulfilled when .v is = i F, that is, when the focus of the 

 imaginary lens EE is jull o,,. lialf ot that of the outer lens 

 N^?; in which cafe the compound focus /will be in the 

 middle of the line OF, and the lens G H placed at half the 

 focal di (lance of the imaginary lens. But it is not necei- 

 fary that the objea, or image of an objeft u v, fliould be 

 fituated in the exterior compound focus i? : this tocus 

 may be fuppofed negative, that is, the image may be 

 between the two lenfes M N and G H, as B A in Z^-. 1 1, 

 which wUl always be the cafe when D is greater than y ; 

 or, IB other words, when the diftai.ce between the two lenfes 

 exceeds the focal diftance of the inner lens G H ; for let 



6X2 



F = 6, D = 4, and y = 2, and wc (hall have -— 



— = «, as in the ftrft isllance. Neither is it neceffary that 

 4 



both the lenfes be convex or planoK:onvex, nor yet with the 

 fame face outwards ; for fuppofe N M concave, when its 

 focus will be negative, or virtually on the oppofite fide of it, and 

 muft be expreiTed by — F ; in this cafe the theorem becomes 



— — — ^ — = X, for the focus of the imaginary lens E E 

 j,_ F- D 



that (hall have its focus equal to the compound focus, which 

 vnU always be pofitive while F + D is greater than y, but 

 when lefs, then negative ; and when j ^ F + D, the rays 

 proceed parallel, and the focus is faid to be infinite. The 



— Fx - Dx 



compound focal diftance in this cafe is — = f, 



and muft be affirmative when x is fo ; but when D = o, then 

 f =■ X. As an example, let the concave N M have a nega- 

 tive focal diilance — F — 3, and let y = 2, while D = i ; 

 then the focal diftance of the imaginary or equal lens will be 



, or - — - = 3 = X, and the compound focal diftance 



2 — 4 — 2 



See Table II. 



Our general theorem may be rendered more extenfive ia 

 its application, by varying it according to the data ; thus. 



will be 



3x3 



I X 7, 



Fx-xD 



r X— X JJ 



if F, X, and D be given to find y, it will be — = = J" » 



to find F with the others given, it will be 



D 



X- y 



= F; 



F>- 



=■ ±=z f. Whence, in 



3 - 3 



this cafe, /o is equal to 2 F O, whereas when N M was con- 

 vex, we had the reverfe, FO = 2/0. When — F = jj, 

 and "D =- 0, i. e. when a concave lens and convex one are 

 placed in contaft, with their feparate focal diftances equal, 

 then X becomes infinite, or, in other words, the rays emerge, 

 and proceed in a parallel direftion ; but if the focal lengths 

 are unequal, there will be a pofitive focus and magnifying 

 power, vvhen the convex has the rtiorter radius; for fup- 

 pofe - F = 3, j» = 2, and D = o, then by the theorem 



F X V n ,1 1 — 6 



p— — , we (hall have — - = 6 = x, and in tliis cafe x = 



/= 6 hkewife. From thefe inftances it will be feen, on 

 examination, that the compound fecal dijlance Of, of the com- 

 bined lenfes, is nothing more than the focal diftance/, found 



by the common geometrical theorem of optics, ■ — f 



d — r •'' 

 adapted to the conftant lens G H, where O F = r, and 

 0P = /, when the rays arc diverging; or Of— — / 



and to find D, there will be F + v = D. From 



X 



thefe analogies we may further obferve, that we have 

 alfo the ratio of the two compound focal diftances to each 

 other, 0/andC/,thus; as/: ?> :: F-Dx^ : .r - U x F; 

 and, therefore, vvhen / = <p, then F = ^ ; or the faid focal 

 diftances can never be equal, but when the lenfes are equal. 

 Laftly, we may obferve, that fince the parallel rays L. G, 

 S H, refrafted through both the combined lenfes, interfeft the 

 axis in the fame point, (f, as it would do if it were refrafted 

 by the fingle lens E E, as is evident by continuing it to R ; 

 therefore, (ince G O — R Q, it will follow that the diameter 

 I K, of the principal pencil of rays K C I, diverging from the 

 focus v", will be the fame as it would have been, if it had 

 proceeded direftly to the fing'e lens E E ; and, coniequent- 

 ly, this combination of lenfes makes no alteration in that 

 refpctl. 



Having now explained how the focal point of any lens, or 

 pair of lenfes, differently circumftanced, may be afcertained 

 by one or other of the dioptric theorems, derived from the 

 refratlive power of glafs agreeably to certain laws cf nature, 

 it will be proper to explain the different fenfcs in which the 

 word focus is applied by optical writers under different cir- 

 cumftances, that our readers may not be at a lofs to know 

 in what fenfe it is to be taken, whenever it occurs in oiu> 

 fubfequent details. The principal or Jolar focus of a lens, is 

 that which is produced by parallel rays coming from an 

 infinite diftance, which that of the fun may be confidered, 

 and when the epithet refralled is added, it has reference to 

 the particular glafs by which the rays are refradled ; but 

 when geometrical is exprefted or underftood, then glafs in 

 jreneral is meant : the virtual, refratled, or geometrical 

 focus, is that which, in a concave glafs, would be formed by 

 the diverging rays continued to a point backwards through 

 the glafs till they meet, and is imaginary rather than real, 

 and generally called negative : the focus arifing from con- 

 verging rays pafling through a convex lens is (horter, or 

 nearer the lens, than the folar focus, and the radiant is fup- 

 pofed to be at a greater than an infinite diftance, if fuch an 

 exprelTion is allowable ; but as no fuch diftance is in nature, 

 converging rays can only be produced by their palTage 

 through a firft lens before they fall on a fecond, which is 

 often the cafe in the conftruftion of optical inftruments : but 

 the focus from diverging rays is always more remote than 

 the folar focus from the lens that produces it ; and, in con- 

 fequence of the reference it has to the fituation of the radi- 

 ant or illuminated objed, is denominated the proper and fome- 

 times the relative focus ; for as the radiant approaches the 

 lens, the proper focus recedes in the fame line, and vice verfJ, 

 as we have more fuUy explained under the article Lens, Be- 

 caufe the radiant and conefponding focus may change places 

 at any time, the two points where they are placed, at oppo- 

 fite fides of the lens, are called the conjugate foci, from their 

 being fo dofely allied, that one cannot move without the 

 other. When the radiant is placed therefore in the pri,nci- 



6 pal 



