23 8 t-low to find tbt Focus of a Lens. [ Book 1 1 L 



rections before and after refraction of a ray patting 

 through the center of a lens are parallel, q EG will re- 

 prefcnt the courfe of one of the incident rays without 

 fenfible crron Parallel to E G draw B R, and in B R 

 produced find the focus V of parallel rays incident on 

 the furface B ; therefore by the firft refra&ion the pa- 

 rallel rays are made to ftrike the fecond furface A* 

 converging to the point V. Join r V* Then one of 

 the rays, which after the firft refraction moved within 

 the glafs in the direction r A, will pafs through the fe- 

 cond furface A, without any refraction, in the direc- 

 tion AV, fmce r A is perpendicular to the fecond fur- 

 face. But E G is the courfe of another ray alfo after 

 the fecond refraction, and G, the point of interfection 

 of thefe two rays> will be the focus of the lens, near 

 to which all the other rays will interfect each other* 

 For all the rays incident on the fecond furface, con-, 

 verging to the point V, by what has been proved of 

 rays refracted by a fingle fpherical furface, will be 

 made to converge to a point between A and V* We 

 have found the point G, as above, for a double convex 

 lens, but the fame mode of reafoning applies to other 

 lenfes, and a fingle infpection of the figjre will fhew 

 whether the rays converge or diverge after the firft re- 

 fraction. 



With E as a center, and EG as radius, defcribe the 

 arc GF. Then if the direction of the parallel rays is 

 changed, the focus will always be in the arc GF, and 

 if the incident rays are parallel to rR, the ?xis of the 

 lens, the principal focus is in F. A double convex 

 and plane convex lens, we have already fecn, make pa- 

 rallel rays to converge; a double concave and plane 

 concave make them diverge. A lens with a concave 

 and convex furface make them converge or diverge, 

 according as the furfaces do or do not interfect each 



other, 



