OPTICAL IMAGES. 



less distinctness than the image formed by the central spot itself, 

 so that by their superposition upon the screen, all will contribute 

 to augment the brightness of the image formed upon it, without 

 producing injurious confusion or indistinctness. But not so with 

 the much more distant and more widely separated images 1, 2, 

 3, 4, &c., produced by the exterior rings of the lenticular surface. 

 These being at very sensible distances from the screen held at 

 the place of the central image would produce a confused, cloudy, 

 and indistinct picture on the screen, which falling 

 upon the more distinct picture produced by the cen- 

 tral part, would give the whole a nebulous and 

 misty appearance, such as is shown in fig. 27, when 

 the object is a circular disc. 



42. It appears therefore that a distinct optical 

 image of an object placed before a convex lens can 

 only be formed when a certain limited part of the 

 central lenticular surface is exposed to the object. The exterior 

 part would render the image brighter by means of the increased 

 light transmitted to it, but at the same time confused by reason 

 of the distance of the place of the distinct image formed by the 

 borders from that formed by the centre. 



The confusion and indistinctness produced in the optical image 

 of an object from the cause here explained and illustrated is 

 called the SPHERICAL ABERRATION. 



43. From what has been explained, it appears that the aberra- 

 tion produced by the central part of the lens is inconsiderable, 

 but that it increases rapidly towards the borders. The extent of 

 the central surface, which is thus free from any considerable 

 aberration depends on the convexity of the lens. If it be but 

 slightly convex, or what is the same, if the radius of the sphere 

 of which it forms a part be great, the extent of this central 

 surface will be considerable ; but as the lens becomes more and 

 more convex, or what is the same, as the radius of the sphere of 

 which it forms a part is less and less, the central part exempt 

 from injurious aberration also becomes less and less. 



44. It follows from this, that in proportion as lenses are more 

 convex, their diameters must be less, inasmuch as otherwise the 

 aberration produced by external parts of their surfaces would 

 destroy the clearness and distinctness of the image. 



Since every increase of the magnifying powers of a lens formed 

 of a given material requires an increase of its convexity, it will 

 also render necessary a decrease of its diameter. 



45. If while the diameter is thus decreased the focal length 

 remained the same, the aperture and consequently the illumina- 

 tion of the image would be diminished. But while the increased 



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