14 



OPTICS. 



one another at these points, and there- 

 fore diverge from them in precisely the 

 same manner as they do from the point 

 MN of the object. Hence we may 

 treat the image n m as a new object, 

 and if we place another lens behind it, 

 an image of n m would be formed in the 

 same manner as if n m were a real ob- 

 ject of the same size. Images of images 

 may therefore be formed in succession 

 by convex lenses, the last image being 

 always considered as a new object, and 

 being always an inverted picture of the 

 one before. 



In order to explain how lenses in- 

 crease the size of objects, and make 

 them appear as if they were brought 

 nearer to us, the reader must understand 

 clearly what is meant by the apparent 

 magnitude of objects. When a shilling 

 is placed a hundred yards from us, it is 

 scarcely visible, and its apparent mag- 

 nitude, or the angle under which it is 

 seen*, is said to be then extremely 

 small. At the distance of twenty or 

 thirty yards, we can just see that it 

 is a round body ; and we see that its 

 apparent magnitude has increased ; at 

 the distance of three yards, we begin 

 to see the King's head upon it ; and at 

 the distance of six or eight inches, its 

 apparent magnitude is so great, that it 

 appears to cover a distant mountain, 

 and we can read both the legend and 

 the date with perfect distinctness. By 

 bringing the smiling nearer the eye, we 

 have actually magnified it, or made it 

 apparently larger ; and though its size 

 remains the same, we have thus made 

 all its parts distinctly seen. 



When the distance of the shilling is 

 twenty feet, let a convex lens, whose 

 focal length is five feet, be placed half 

 way between the shilling and the eye, 

 that is, ten feet from each: then it 

 is demonstrable that the image of the 

 shilling formed by the lens will be ex- 

 actly of the same size as the shilling, 

 and, consequently, it is not directly 

 magnified by the lens ; but, as the 

 image is brought so near us that the 

 eye can view it at the distance of six 

 inches, its apparent magnitude is in- 

 creased in the proportion of six inches 

 to twenty feet, or as one to forty, that is, 

 forty times. Hence, we have magnified 

 the shilling forty times merely by bring- 

 ing an image of it near to the eye. 



If the shilling, or object, is so remote 

 that we cannot place a lens half way 



* T he angle M C N is the angle under which the 

 object M N is seen to an eye at C, in/fy. 14, 



between it and the eye, we can still 

 magnify it by forming a small image of 

 it in the following manner : Let the same 

 lens of five feet focal length, like L L, 

 (fig. 14.) be placed in a hole in the 

 window- shutter of a dark room, and 

 let us suppose that the object, such as a 

 church-spire, is distant 5000 feet, or 

 about a mile ; then, as the rays from 

 this object will fall nearly parallel on 

 the lens LL, an inverted image nm 

 will be formed in its principal focus, or 

 five feet behind the lens, and the size of 

 this image will be to that of the object 

 as 5 feet is to 5000, or 1 000 times smaller 

 than the object. But if we view this 

 small image, so as to see it distinctly, at 

 the distance of six inches, we see it 

 under an angle, or with an apparent 

 magnitude, as much greater than if the 

 same small image were equally far off 

 with the spire, as 6 inches is to 5000 feet, 

 that is, 1 0,000 times. Hence, though the 

 image is 1000 times less than the spire, 

 from one cause, yet from its being 

 brought near to the eye, it is 1 0,000 times 

 greater in apparent magnitude ; conse- 

 quently, its apparent magnitude is in- 

 creased VoVo or ten times, that is, it is 

 actually magnified ten times by means of 

 the lens L L. This magnifying power is 

 always equal to the focal length of the 

 lens, divided by the distance at which 

 the eye sees near objects most dis- 

 tinctly, which in the present example is 



5 feet Of 60 inches or ^ as 



6 inches 6 inches 

 before. 



When the image n m is received upon 

 any smooth and white surface, such as 

 paper, stucco, ground glass, &c. then the 

 lens, and other apparatus, is called a 

 camera obscura, or dark chamber ; but 

 when the eye is placed behind the lens, 

 and sees the inverted image in the air, the 

 apparatus is a telescope, from two Greek 

 words signifying to see at a distance, 

 though this name is commonly given 

 only when there are two or more lenses. 



But there is another method of mag- 

 nifying objects, particularly objects 

 within our reach, which is of great im- 

 portance in optics. We all know that 

 the eye can see objects distinctly when 

 placed at a great distance, that is, when 

 the rays proceeding from the object are 

 parallel, or nearly so. Consequently, 

 if we place an object very near the eye, 

 so as to give it great apparent magni- 

 tude, and if we can by any means make 

 the rays which flow from it enter the eye 

 nearly parallel to each other, we must 



