OPTICAL IMAGES, 
Fig. 27. 
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, &e., 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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