ELEMENTS OF THE WAVE-THEORY OF LIGHT. CHAPTER I. PROPAGATION OF LIGHT. (1) NATURAL bodies may be divided into two classes in relation to Light. Some possess, in themselves, the power of exciting the sense of vision, and of producing the sensation of light; while others are devoid of that property. Bodies of the former class are said to be luminous; those of the latter, non-luminous. The Sun and the fixed stars are all luminous bodies; terrestrial bodies are luminous, in the states of incandescence, combustion, or phosphorescence. Non-luminous bodies acquire the power of exciting the sensation of light in the presence of a luminous body. Thus, a lamp or candle illuminates all the objects in a room, and renders them visible; and the light of the Sun illuminates the Earth and the planets. This property of bodies is due to their capacity of reflecting light, and belongs to them in different degrees. (2) The foregoing distinction of bodies, obvious as it seems, was not fully comprehended by the ancients. According to B them, vision was performed by something which emanated from the eye to the object; and the sense of Sight was explained by the analogy of that of Touch. In this view, then, the sensation was represented as independent of the nature of the body seen; and all objects should be visible, whether in the presence of a luminous body or not. This strange hypothesis held its ground for many centuries. The Arabian astronomer, Alhazen, who lived in the latter part of the eleventh century, seems to have been the first to refute it, and to prove that the rays which constituted vision came from the object to the eye. (3) The light of a luminous body emanates from it in all directions. Thus, the light of a lamp or candle is seen in all parts of a room, if nothing intervenes to intercept it; and the light of the Sun illuminates the Earth, the Planets, and their satellites, in whatever position they may be placed respecting it. Each physical point of a luminous body is an independent source of light, and is called a luminous point. (4) Non-luminous bodies are distinguished into two classes, according as they allow the light which falls upon them to pass freely through their substance, or intercept it. Bodies of the former kind are said to be transparent; those of the latter, opaque. There are no bodies in nature actually corresponding to these extremes. The most transparent bodies, as air and water, intercept a sensible quantity of light, when of sufficient thickness; and, on the other hand, the most opaque bodies, such as the metals, allow a portion of light to pass through their substance, when reduced to laminae of exceeding tenuity. (5) In the same homogeneous medium, light is propagated in right lines, whether it emanates directly from luminous bodies, or is reflected from such as are non-luminous. This is proved by the fact that when an opaque body is interposed in the right line connecting the eye and the luminous source, the light of the latter is intercepted, and it ceases to be visible. The same thing is proved also by the shadows of bodies, which, when received upon plane surfaces perpendicular to the path of the light, are observed to be similar to the section of the body which produces them. This property of light was recognised by the ancients; and by means of it the few optical laws which were known to them became capable of mathematical expression and reasoning. Any one of these lines, proceeding from a luminous point, is called in optics a ray. (6) In a perfectly transparent medium, the intensity of the light proceeding from a luminous point varies inversely as the square of the distance. This is easily proved, if light be supposed to be a material emanation of any kind. For the intensity of the light, received upon any spherical surface whose centre is the luminous point, is as the quantity of the light directly, and inversely as the space over which it is diffused. But none of the light being lost, the quantity of light received upon any spherical surface is the same as that emitted, and is therefore constant; and the space of diffusion, or the area of the spherical surface, is as the square of its radius. Hence the intensity of the light is inversely as the square of the radius, i. e. inversely as the square of the distance. Let the light be supposed to emanate from the points of an uniformly luminous surface, which we shall suppose to be a small portion of a sphere. Then the quantity of light emitted is proportional to the quantity emitted by a single point, and the number of points (or area) conjointly. Hence if a denote the area of the luminous surface, and i the quantity emitted from a single point, which is a measure of the absolute brightness, the intensity of the illumination, at any distance d, is ai d2 (7) A plane surface, whose dimensions are small in comparison with the distance, and which is perpendicular to the incident light, may, without sensible error, be considered as a portion of a spherical surface concentric with the luminary. The intensity of the illumination, therefore, or the quantity of light received upon a given portion of such a plane, is expressed by the formula of the preceding Article. When the surface is inclined to the incident light, the quantity of the light received by any given portion is diminished in the ratio of unity to the sine of the angle of inclination. The intensity of the illumination is, therefore, diminished in the same proportion, and is expressed by the formula ai sin 0 being the inclination of the surface to the incident light. (8) Experience proves that the eye is incapable of comparing directly two lights, so as to determine their relative intensities. But, although unable to estimate degrees, the eye can detect differences of intensity with much precision; and with this power it is enabled (by the help of the principles just established) to compare the intensities of two lights indirectly. Let two portions of the same paper, or any similar reflecting surface, be so disposed, that one of them shall be illuminated by one of the lights to be compared, and the other by the other, the light being incident upon each at the same angle. Then let the distance of one of the lights be altered, until there is no longer any appreciable difference in the inten |