12 



OPTICS. 



to make large burning glasses; and, 

 on this account, Dr. Brewster has con- 

 trived a built-up lens, which may be 

 made of any magnitude, and which is 

 superior to a common lens of the same 

 size. - 



The property of a convex lens, by 

 which rays proceeding from its focus 

 are refracted into parallel directions, 

 enables us in light-houses to throw a 

 strong light to great distances at sea. 

 To this purpose the built-up lens above- 

 mentioned has been applied with great 

 success*. 



CHAPTER IV. DIOPTRICS continued. 



Formation of Images by Lenses Vision 

 of Images Apparent^ Magnitude 

 Magnifying Power Telescopes < 

 Microscopes. 



WE have already shown in Chapter I., 

 that a tolerably distinct image or pic- 

 ture of any object may be formed upon 

 a piece of paper, by placing a small pin- 

 hole or other aperture between the ob- 

 ject and the paper, and excluding all ex- 

 traneous light. Thus, if C, (fig. 13.) is a 

 small hole in the front of a box, A B m n, 



and M N an object before it, the rays 

 from the end M will pass straight 



Fig. 13. 



through the hole C, and illuminate the 

 point m of the back of the box with their 

 own colour ; the rays from N will do 

 the same at n ; and all other points of 

 M N will in like manner throw their 

 rays on points immediately opposite 

 them between m and n. The effect of 

 the small hole C is to prevent the rays 

 from any one point of the object M N 

 from falling on any other point in m n, 

 than the point immediately opposite to 

 it ; and hence the smaller that we make 

 the aperture C, the more dictinct will be 

 the picture mn of the object M N. 

 But from the same cause the picture 

 will be faint, as the hole C admits such 

 a small number of the rays which 

 flow from every point of the object 

 M N. If we enlarge the hole C, and 

 substitute a lens L L, as in Jig. 14, 



having L n for the focal distance suited 

 to the distance of M N, we shall have 

 an image n m every way similar to 

 that formed by the hole, but much 

 brighter and more distinct. Since all 

 the rays which flow from M, such as 

 M L, M L, and fall upon the lens L L, 

 will be refracted to a focus at m, and all 

 those from N to a focus at n, they will 

 there paint a distinct picture of the 

 points from which they come, and con- 

 sequently of the whole object M N. 

 The superior distinctness of the image 

 nm in fig. 14, to that formed by the 

 aperture C in/,g-. 13, arises from the cir- 

 cumstance that the rays from one point 

 of the object M N cannot interfere with 

 those from any other point ; and its su- 

 perior brightness arises from the great 

 number of rays from each point which 



are collected by the lens in the corre- 

 sponding point of the image. 



It is obvious from the figure, that the 

 image n m formed by a convex glass 

 must necessarily be * inverted, for it is 

 impossible that the rays from the upper 

 end M of the object can be carried by re- 

 fraction to the upper end of the image at n. 



As the rays M C, N C are refracted 

 in lines C m, C n, parallel to C N, C M, 

 the triangles n C m, N C M are similar, 

 and m n is to M N as C m is to C M, 

 that is, the length of the image formed 

 by a convex lens is to the length of the 

 object, as the distance of the image is to 

 the distance of the object from the lens. 



The relative positions of the object 

 and image when the object is placed at 

 different distances from the lens, are 

 exactly the same as the conjugate foci of 



* See the Chapter on PHOTOMETRY in the next Treatise, where this subject will Lc 



