OPTICS. 



ther glass, F G, of the same convexity as 

 D E, be placed in the rays at the same 

 distance from the focus, it will refract 

 them so, as that, after going out of it, 

 they will be all parallel, as b c; and go on 

 in the same manner as they came to the 

 first glass, D E, but on the contrary sides 

 of the middle ray. The rays diverge 

 from any radiant point, as from a principal 

 focus; therefore, if a candle be placed at 

 f, in the focus of the convex glass F G, 

 the diverging rays in the space F/G will 

 be so refracted by the glass, that, after 

 going out of it, they will become paral- 

 lel, as shewn in the space c b. If the 

 candle be placed nearer the glass than its 

 focal distance, the rays will diverge, after 

 passing through the glass, more or less, as 

 the candle is more or less distant from the 

 focus. 



If the candle be placed further from 

 the glass than its focal distance, the rays 

 will converge, after passing through the 

 glass, and meet in a point, which will 

 be more or less distant from the glass, 

 as the candle is nearer to, or further 

 from, its focus; and where the rays 

 meet, they will form an inverted image of 

 the flame of the candle; which may be 

 seen on a paper placed in the meeting of 

 the rays. 



Hence, if any object, ABC (fig. 6), 

 be placed beyond the focus, F, of the 

 convex glass, d e f, some of the rays 

 which flow from every point of the ob- 

 ject, on the side next the glass, will fail 

 upon it, and after passing through it, 

 they will be converged into as many 

 points on the opposite side of the glass, 

 where the image of every point will be 

 formed, and consequently the image of 

 the whole object, which will be invert- 

 ed. Thus the rays, A d, A e, A/, flow- 

 ing from the point A, will converge in 

 the space, daf, and by meeting at o, will 

 there form the image of the point A. The 

 rays, B d, B e, B/, flowing from the point, 

 B, will be united at b, by the refraction 

 of the glass, and will there form the 

 image of the point, B. And the rays, 

 C d, C c, C/, flowing from the point, C, 

 will be united at c, where they will form 

 the image of the point, C. And so of 

 all the intermediate points between A 

 andC. 



If the object, A B C, be brought near- 

 er to the glass, the picture, a b c, will be 

 removed to a greater distance ; for then, 

 more rays flowing from every single 

 point, will fall more diverging upon the 

 glass; and therefore cannot be so soon col- 

 lected into the corresponding points be- 



hind it. Consequently, if the distance of 

 the object, ABC (fig. 7), be equal to the 

 distance, e B, of the focus of the glass, 

 the rays of each pencil will be so refrac- 

 ted by passing through the glass, that they 

 will go out of it parallel to each other ; as 

 d I, e H,/h, from the point C ; d G, e K, 

 /I), from the point B ; and dK, e E./L, 

 from the point A ; and therefore there 

 will be no picture formed behind the 

 glass. 



If the focal distance of the glass, and 

 the distance of the object from the glass, 

 be known, the distance of the picture 

 from the glass may be found by this rule, 

 itiz. multiply the distance of the focus 

 by the distance of the object, and di- 

 vide the product by their difference ; the 

 quotient will be the distance of the pic- 

 ture. 



The picture will be as much bigger, or 

 less, than the object, as its distance from 

 the glass is greater or less than the dis- 

 tance of the object : for (fig. 6) as B e is 

 to eb t so is A C to c a ; so'that if ABC 

 be the object, c b a will be the picture ; or 

 if c b a be the object, ABC will be the 

 picture. 



If rays converge before they enter a 

 convex lens, they are collected at a point 

 nearer to the lens than the focus of paral- 

 lel rays. If they diverge before they en- 

 ter the lens, they are then collected in a 

 point beyond the" focus of parallel rays ; 

 unless they proceed from a point on the 

 other side at the same distance with the 

 focus of parallel rays ; in which case they 

 are rendered parallel. 



If they proceed from a point nearer than 

 that, they diverge afterwards, but in a 

 less degree than before they entered the 

 lens. 



When parallel rays, as a b c d e (fig. 8), 

 pass through a concave lens, as A B, they 

 will diverge after passing through the 

 glass, as if they had come from a radiant 

 point, C, in the centre of the convexity of 

 of the glass ; which point is called the 

 " virtual, or imaginary focus." 



Thus, the ray, a t after passing through 

 the glass, A. B, will go on in the direction, 

 k /, as if it had proceeded from the point, 

 C, and no glass been in the way. The 

 ray, b, will go on in the direction, m n / 

 the ray, c, in the direction, op, &.c. The 

 ray, C, that falls directly upon the middle 

 of the glass, suffers no retraction in pass- 

 ing through it, but goes on in the same 

 rectilinear direction, as if no glass had 

 been in the way. 



If the glass had been concave only on 

 nie side, and the other side qnite flat, the 



