Chap.- 6.] Plano-convex and concave Lenfis. 23? 



the firft refrafHon. This point m is the center of the 

 lens, and in the two cafes before us it bifects the thick- 

 nefs of the lens ; far fmce the triangles C I m, dm are 

 firnilar, C I : ci :: Cm \ cm and as C I and ci are 

 equal C ;;/ and cm are equal, and confequently nm and 

 mo are equal. If the radii' were not equal, the center 

 of the lens is neareft to that furface whofe radius is the 

 leaft, and its place may be accurately found by the 

 preceding oroportion. 



In Plate XVIII. Fig. 26, 27. reprefent two !enfes> 

 the one v/i h a plane and a convex furface, the other 

 with a plane and a concave furface. In both cafes the 

 center of the lens will be at m in the fpherical furface^ 

 for the point may be confidered as in the tangent to 

 the circle at m, which is parallel to A IB, therefore the 

 ray I / makes equal angles of incidence at the points I 

 and z, and confequently the angles of refraftion will bd 

 equal. From the proportion aifo difcovered in convex 

 or concave lenfes, the fame truth is evident; for as we 

 increafe the radius of A I B, the point m (Fig. 24, 2,5.) 

 approaches nearer to ; and as this radius may be in- 

 creafed without limit, the diftance of mn may be.de- 

 creafed without limit, fo that evidently the nearer the 

 circle approaches to a plane figure, the nearer will be 

 the approach of m to ;/. 



Plate XVIIL Fig. 28. reprefents a lens with one 

 furface concave the other convex, in which cafe the 

 point m will be without the lens. 



Having found the" center of a lens, we are next to 

 find its principal focus or point, from which parallel rays, 

 after refraclion, appear to diverge, or to which they 

 converge. Let AB (Plates XVIII. XIX. Fig. 2.9, 

 30, 31, 32; 33, 34) reprefent a lens, whofe center is E, 

 and the centers of the llirfa'tes R and r, and let q E G 

 be drawn parallel to the incident rays ; then as the di- 



rewlions 



