The first diagram exhibits the comparative size of a hole one seventy-fifth of an inch in diameter, and the longest light-waves. If we limit the aperture of the eye to this size, by holding a sheet of writing-paper before it, with such a needle-hole pricked in it, and look through the hole at a luminous point, such as a distant electric light, instead of seeing it as a point of light too small to have a visible surface, as we should expect, we will see instead quite a large disk of light surrounded by one or two bright rings as illustrated in Diagram 5.
This peculiar appearance is caused by the spreading of the light-waves, after passing through the needle-hole, so that, although the wave-fronts are spherical as they emerge from the lens of the eye, yet at the distance of the retina they have spread out sidewise so much that, instead of running to a point, they cover a surface large enough to be distinctly perceived as a luminous disk. It can be proved mathematically by the theory of undulations, that the diameter of this luminous disk, measured in seconds of arc as viewed from the center of any lens, for light-waves, having a length of about 1⁄500000 of an inch (the brightest and central part of the normal spectrum), will equal four and a half divided by the number of inches in the clear aperture of the lens, its size, however, increasing or diminishing a very little, according as the light-waves are longer or shorter.
Objects viewed through such a small hole appear very indistinct, from the image of each point overlapping those of its neighbors. The same defective vision would have resulted had the light-waves been created less minute than they are, or of a size comparable to the diameter of the pupil of the eye.
It is also on account of the extreme minuteness of these waves that light appears to travel in rays, and that opaque bodies throw sharply defined shadows.
Returning to a simple lens of considerable diameter, as shown in Diagram 6, and still assuming it to have spheroidal surfaces so that the emerging wave-fronts shall be spherical, and considering the light-waves to be originated by a single vibrating molecule situated at an infinite distance, we come to a peculiar phenomenon, also a result of the excessive minuteness of the light-waves, and the consequent tend-