3. That a luminous point, by some unknown power, sends forth rays of light in all directions, and is the center of a sphere of light, which extends indefinitely on all sides; and if we conceive some of these rays to be intercepted by a plane, then is the luminous point the summit of a pyramid, whose body is formed by the rays, and its base by the intercepting plane. The image of the surface of an object, which is painted on the wall, is also the base of a pyramid of light, the apex of which is the hole; the rays which form this pyramid, by crossing at the hole, form another, similar and opposite to this, of which the hole is also the summit, and the surface of the object the base.
4. That an object is visible, because all its points are radiant points.
5. That the particles of light are indefinitely small; for the rays, which proceed from the points of all the objects opposite to the hole, pass through it, though extremely small, without embarrassing or confounding each other.
6. That every ray of light carries with it the image of the object from which it was emitted.
The nature of vision in the eye may be imperfectly illustrated by the experiment of the darkened room; the pupil of the eye being considered as the hole through which the rays of light pass, and cross each other, to paint on the retina, at the bottom of the eye, the inverted images of all those objects which are exposed to the sight, so that the diameters of the images of the same object are greater, in proportion to the angles formed at the pupil, by the crossing rays which proceed from the extremities of the object; that is, the diameter of the image is greater, in proportion as the distance is less; or, in other words, the apparent magnitude of an object is in some degree measured by the angle under which it is seen, and this angle increases or diminishes, according as the object is nearer to, or farther from the eye; and consequently, the less the distance is between the eye and the object, the larger the latter will appear.
From hence it follows, that the apparent diameter of an object seen by the naked eye, may be magnified in any proportion we please; for, as the apparent diameter is increased, in proportion as the distance from the eye is lessenned, we have only to lessen the distance of the object from the eye, in order to increase the apparent diameter thereof.[24] Thus, suppose there is an object, A B, [Plate I.] Fig. 1, which to an eye at E subtends or appears under the angle A E B, we may magnify the apparent diameter in what proportion we please, by bringing our eye nearer to it. If, for instance, we would magnify it in the proportion of F G to A B; that is, if we would see the object under an angle as large as F E G, or would make it appear the same length that an object as long as F G would appear, it may be done by coming nearer to the object. For the apparent diameter is as the distance inversely; therefore, if C D is as much less than C E, as F G is greater than A B, by bringing the eye nearer to the object in the proportion of C D to E D, the apparent diameter will be magnified in the proportion of F G to A B; so that the object A B, to the eye at D, will appear as long as an object F G would appear to the eye at E. In the same manner we might shew, that the apparent diameter of an object, when seen by the naked eye, may be infinite. For since the apparent diameter is reciprocally as the distance of the eye, when the distance of the eye is nothing or when the eye is close to the object at C, the apparent diameter will be the reciprocal of nothing, or infinite.
[24] Rutherforth’s System of Natural Philosophy, p. 330.
There is, however, one great inconvenience in thus magnifying an object, without the help of glasses, by placing the eye nearer to it. The inconvenience is, that we cannot see an object distinctly, unless the eye is about five or six inches from it; therefore, if we bring it nearer to our eye than five or six inches, however it may be magnified, it will be seen confusedly. Upon this account, the greatest apparent magnitude of an object that we are used to, is the apparent magnitude when the eye is about five or six inches from it: and we never place an object much within that distance; because, though it might be magnified by these means, yet the confusion would prevent our deriving any advantage from seeing it so large. The size of an object seems extraordinary, when viewed through a convex lens; not because it is impossible to make it appear of the same size to the naked eye, but because at the distance from the eye which would be necessary for this purpose, it would appear exceedingly confused; for which reason, we never bring our eye so near to it, and consequently, as we have not been accustomed to see the object of this size, it appears an extraordinary one.
On account of the extreme minuteness of the atoms of light, it is clear, a single ray, or even a small number of rays, cannot make a sensible impression on the organ of sight, whose fibres are very gross, when compared to these atoms; it is necessary, therefore, that a great number should proceed from the surface of an object, to render it visible. But as the rays of light, which proceed from an object, are continually diverging, different methods have been contrived, either of uniting them in a given point, or of separating them at pleasure: the manner of doing this is the subject of dioptrics and catoptrics.
By the help of glasses, we unite in the same sensible point a great number or rays, proceeding from one point of an object; and as each ray carries with it the image of the point from whence it proceeded, all the rays united must form an image of the object from whence they were emitted. This image is brighter, in proportion as there are more rays united; and more distinct, in proportion as the order, in which they proceeded, is better preserved in their union. This may be rendered evident; for, if a white and polished plane be placed where the union is formed, we shall see the image of the object painted in all its colours on this plane; which image will be brighter, if all adventitious light be excluded from the plane on which it is received.