OPTICAL INSTRUMENTS. 



making a greater angle with the perpen- 

 dicular to the flat side, as it now enters 

 a rarer medium. 



(7.) If, instead of supposing the object 

 at an infinite distance, and consequently 

 a point, we imagine it removed to some 

 finite distance, a like action in a pro- 

 portional degree will be observed, only 

 the object will not be reduced to a point, 

 but its image will be formed at F,'whose 

 size is equal to the angle under which 

 the object would be seen without the 

 lens. Let a c (fig. 7.) be the object, 

 and b the lens: now, this object will 

 subtend the angle a b c from every 

 portion of the lens, and an inverted 

 image d e will be formed under the 

 equal angle d b e ; for whenever right 

 lines intersect each other, the opposite 



angles are always equal. This experi- 

 ment may be proved by a common 

 convex glass lens. Suppose the distance 

 of the focal point is six inches, and the 

 lens two inches in diameter, the image 

 of a distant object may be seen on a wall 

 when the lens is held a little more than 

 its focal length from it ; then let the size 

 of the image be measured : now remove 

 the lens, and measure the apparent size 

 of the object, while the eye of the ob- 

 server is in its place, taking the distance 

 of the focus of the lens for the point of 

 measurement, and it will be found of 

 the same size in both cases. If a wafer 

 is made to adhere to the surface of the 

 lens, so as to stop a portion of the light, 

 the size is not altered, but the image 

 will be formed less bright. 



Fig. 7. 



(8.) When an object is placed in the 

 focus of a lens, the rays diverging from it 

 will, by the action of the lens, be rendered 

 parallel ; this case, however, is only the 

 reverse of the former, the place of the 

 object and image being changed. But 

 this astonishing circumstance will take 

 place : when observed on the side for 

 parallel rays, the objects will appear 

 magnified or increased in size, should 

 the distance of the object from the lens 

 be less than the eye can see it without. 

 Let a b (fig. 8.) be the nearest distance 

 at which an object can be seen distinctly 



without the assistance of a lens, and b d, 

 the distance of the object when seen 

 through the lens, equal to half the 

 distance a b ; now the angle c bg, which 

 the object subtended without the lens, 

 is only half the angle e bf- and, there- 

 fore, the object will be magnified twice, 

 when seen by the lens ; and if the dis- 

 tance had been only , j, ^o, the object 

 would have been magnified 3, 4, or 10 

 times in length and breadth, and, conse- 

 quently, its surface increased 9, 16, or 

 100 times. 



(9.) Concave lenses obey the samelaws 

 of refraction as convex, but as the cur- 

 vature is reversed, the rays are bent out- 

 wards ; hence a concave lens will ren- 

 der parallel rays diverging, as may be 



seen in fig. 9, where a is the object, a b 

 rays proceeding parallel to each other 

 from the object. These rays, when 

 transmitted by the concave lens, are 

 made to diverge, as if they came from 



