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42 Concerning the Refractions Chap.7. furface A, the emergent rays muft have their focus in fome point of that ray which paffes Straight through this furface; that is in the line Vr, drawn through its center r: and fince the whole courfe of * Art. 97. another ray is reckoned a ftraight line gEG\ its interferon G with Vr determines the focus of them all. Q^ E. D. 99. Corol. 1. When the incident rays are parallel to the axis rR, the focal diftance EF is equal to EG. For let the incident rays that were parallel to gE be gradually more inclined to the axis till they become parallel to it; and their firft and fecond focufes /^and G will defcribe circular arches FT and GF whofe centers are R and E. For the line R V is invariable; being in proportion to RB in a given ratio of the leffer of the fines of incidence and refraction to their 'Art. 92. difference b; confequently the line £ G is alfo invariable, being in proportion to the given line i?^"in the given ratio of rE to rR, becaufe the triangles EGr, RVr are equiangular. 100. Corol. 2. The laft proportion gives the following rule for finding the fo:al diftance of any thin lens. As Rr, the interval between the centers of the furfaces, is to rE, the femidiameter of the Second furface, fo is R V or R T, the continuation of the firft femidiameter to the firft focus, to EG or EF, the focal diftance of the lens. Which according as the lens is thicker or thinner in the middle than at its edges, muft lye on the fame fide as the emergent rays or the oppofite fide. 101. Corol. 3. Hence when rays fall parallel on both fides of any lens, the focal diftances ££, Ef'are equal. For let rt be the continuation of the femidiameter £ r to the firft focus / of rays falling parallel upon the furface A; and the fame rule that gave rR to rE as RT to EF, gives alfo rR to RE as rt to Ef. Whence Ef and EFave equal, becaufe the rectangles under rE, R T and alfo under RE, rt ate equal. For rE is to rt and alfo RE to RT in the fame cA.t. 92. given ratioc. 102. Corol. 4. Hence in particular in a doubleconvex or double concave lens made of glafs, it is as the fum of their femidiameters (or in a menifcus as their difference) to either of them, fo is double the other, to the focal diftance of the glafs. For the continuations RT, rt are feverally double their femidiameters: becaufe in glafs "Art. 93.13. £7 is t0 qji ;inci a]f0 Et to tr as 2 to 2 d. 103. Corol. 5. Hence if the femidiameters of the furfaces of the glafs be equal, its focal diftance is equal to one of them; and is equal to the local diftance of a planoconvex or planoconcave glafs whofe femidiameter is as Short again. For considering the plane furface as having an infinite femidiameter, the firft ratio of the laft mentioned proportion may be reckoned a ratio of equality. Pro
Object Description
Title  The elementary parts of Dr. Smith's Compleat system of opticks. 
Alternative Title  The elementary parts of Dr. Smith's Compleat system of opticks : selected and arranged for the use of students at the universities : to which are added... explanatory propositions from other authors. 
Reference Title  Smith, Robert, 1778. The elementary parts of Dr. Smith's Compleat system of opticks. 
Creator  Smith, Robert, 16891768 
Subject  Optics  Early works to 1800. 
Publisher  Cambridge : Printed by J. Archdeacon, Printer to the University ; and sold by T. & J. Merrill and 7 others. 
DateOriginal  1778 
Format  JP2 
Extent  28 cm. 
Identifier  col150 
Call Number  QC353.S515 1778 
Language  English 
Collection  Color and Optics 
Data contributor  Linda Hall Library, LHL Digital Collections. 
Description
Title  Page 42. 
Format  tiff 
Identifier  col150072 
Rights  http://www.lindahall.org/imagerepro/terms/ 
Type  image 
OCR Transcript  42 Concerning the Refractions Chap.7. furface A, the emergent rays muft have their focus in fome point of that ray which paffes Straight through this furface; that is in the line Vr, drawn through its center r: and fince the whole courfe of * Art. 97. another ray is reckoned a ftraight line gEG\ its interferon G with Vr determines the focus of them all. Q^ E. D. 99. Corol. 1. When the incident rays are parallel to the axis rR, the focal diftance EF is equal to EG. For let the incident rays that were parallel to gE be gradually more inclined to the axis till they become parallel to it; and their firft and fecond focufes /^and G will defcribe circular arches FT and GF whofe centers are R and E. For the line R V is invariable; being in proportion to RB in a given ratio of the leffer of the fines of incidence and refraction to their 'Art. 92. difference b; confequently the line £ G is alfo invariable, being in proportion to the given line i?^"in the given ratio of rE to rR, becaufe the triangles EGr, RVr are equiangular. 100. Corol. 2. The laft proportion gives the following rule for finding the fo:al diftance of any thin lens. As Rr, the interval between the centers of the furfaces, is to rE, the femidiameter of the Second furface, fo is R V or R T, the continuation of the firft femidiameter to the firft focus, to EG or EF, the focal diftance of the lens. Which according as the lens is thicker or thinner in the middle than at its edges, muft lye on the fame fide as the emergent rays or the oppofite fide. 101. Corol. 3. Hence when rays fall parallel on both fides of any lens, the focal diftances ££, Ef'are equal. For let rt be the continuation of the femidiameter £ r to the firft focus / of rays falling parallel upon the furface A; and the fame rule that gave rR to rE as RT to EF, gives alfo rR to RE as rt to Ef. Whence Ef and EFave equal, becaufe the rectangles under rE, R T and alfo under RE, rt ate equal. For rE is to rt and alfo RE to RT in the fame cA.t. 92. given ratioc. 102. Corol. 4. Hence in particular in a doubleconvex or double concave lens made of glafs, it is as the fum of their femidiameters (or in a menifcus as their difference) to either of them, fo is double the other, to the focal diftance of the glafs. For the continuations RT, rt are feverally double their femidiameters: becaufe in glafs "Art. 93.13. £7 is t0 qji ;inci a]f0 Et to tr as 2 to 2 d. 103. Corol. 5. Hence if the femidiameters of the furfaces of the glafs be equal, its focal diftance is equal to one of them; and is equal to the local diftance of a planoconvex or planoconcave glafs whofe femidiameter is as Short again. For considering the plane furface as having an infinite femidiameter, the firft ratio of the laft mentioned proportion may be reckoned a ratio of equality. Pro 