Reflection — Refraction — Dispersion.— When light waves originating at a point fall upon a surface separating two media, the sys tem of waves is broken up into two systems, one of which remains in the first medium, though moving in a changed direction, and the other entering the second medium. The former system constitutes reflected light, and the latter, also in general changed in direction, is called refracted light. If the bounding surface is smooth the phenomena of reflection and of re fraction are regular and the modified paths of the light can be calculated. The total intensity of the reflected light varies greatly with the nature of the media on either side the interface and also upon the angle at which the wave sur faces meet this surface. If we consider only the case of the first medium being air, we may describe two general cases of interest. (I) If the second medium is a transparent substance, like most liquids, ice, glass, etc., the reflected light is ordinarily of small intensity as com pared to the incident light, but increases with increasing angle of incidence, until, as this angle approaches 90 degrees, the rate of increase be comes very great. (2) If the second medium is a metal the reflected light is ordinarily a large portion of the whole, but its intensity does not vary greatly with the angle of incidence. Turning now to a consideration of the light which passes the interface and enters the second medium we find that in some substances these waves will go a great distance without notable diminution of intensity. Such substances are called transparent. In others, described as opaque, the light waves are converted into other forms of energy in longer or shorter dis tances, and are destroyed as light. In the case of metals and other good conductors of electric ity this destruction follows a penetration of only a few millionths of an inch. The laws which determine the directions of the reflected and refracted light are simple. Let us call the angles which the incident, the reflected and the refracted waves make with the surface separat ing the two media, the angles respectively of incidence, of reflection and of refraction. For the law of reflection, the angle of reflection is then equal to the angle of incidence. For re fraction, the sine of the angle of incidence divided by the sine of the angle of refraction is equal to the velocity of the propagation of the waves in the first medium, divided by the velocity is the second medium. The angle of incidence being the polarizing angle for trans parent substances, the tangent of the polar izing angle equals the index of refraction. This is known as Brewster's law. These laws are not absolutely without geometrical am biguity, but are made so by the addition that he change of direction in both cases is the least possible. If the refracted light is ob served critically it will be found that the di rection varies somewhat for lights of different colors, so that, if white light is incident, the light will be arranged in direction according to its component colors, the red being least changed, then yellow, green, blue, and, most of all, violet. This phenomenon is called dis persion. Since the maximum difference of de viation for small angles of incidence is never mbre than a small part of the whole — very few substances exhibiting a ratio greater than one twentieth — dispersion should be regarded as a secondary phenomenon of refraction.
Optical Images — Optical Instruments.— When light waves originating at a point are modified by one or more smooth surfaces— either by reflection, or refraction, or by a com bination of the two—so that after these modi fications they either pass through a new point or seem to do so, this new point is called the optical image of the first. To distinguish the cases of real points from those which only ap pear to be new centres, the terms real image and virtual image are employed.
If an optical system can form an image, real or virtual, of a point, it follows from the law of continuity that it will also form simultaneous images of near lying points with a like degree of precision; the images of remoter points, however, may be, and in general will be, im perfect. The simplest of all optical systems is a plane mirror, and it is the only optical in strument which is absolutely perfect, provided only that it is not of too small dimensions. Such an instrument forms virtual images of all points in front of it, the sources and images being symmetrically placed with reference to the plane of the mirror. Bodies of transparent substances bounded by smooth curved surfaces, ordinarily spherical surfaces, are called lenses. Almost all optical instruments lenses for producing the required modification on transmitted light. If a lens increases the curva ture of the wave-surfaces which pass through it — which in general requires the middle of the lens to be thicker than its periphery — it will produce real images of remote objects near its geometrical axis. Suoh a lens is called a positive-lens. A screen to receive the images and an opaque enclosure to shield it from ex traneous light constitutes the important instru, ment known as the camera obscura. One of the earliest optical instruments invented, it has only been of importance since the discovery of a method of fixing the images a short time before the middle' of the last century. The re quirements of modern photography, especially the demand for brightness and wide angular extent in the images, have led to inventions of wonderfully complex camera lenses, so that ordinarily they are made of combinations of from 4 to 10 different lenses, involving two or three different kinds of glass in their con struction.
The eye is properly a camera obscura, in which images of objects neither too near the observer nor too far from the axis of vision are formed upon the retina as a screen. The most important difference between the eye and the photographic camera lies in the fact that the interior of the eye is filled with a substance optically different from air, which introduces some remarkable modifications in the phenom ena of vision. These may be ignored in this casual review of the construction and func tion of optical instruments.
In almost all optical systems, excepting the camera obscura, the eye is a necessary part in use, and it is, therefore, convenient to specify the conditions under which distinct vision is possible. To a normal eye, any object very near the axis of vision can be distinctly seen if it lies at a distance comprised between five or six inches for a nearer limit and infinity for the farther. Thus, the moon and a printed page held at the customary distance for reading can be seen equally well. We shall assume a distance of 10 inches as a standard of comparison.
If a small ob ject be brought quite close to the eye it will appear larger, but when too close vision will be indistinct. This js because the refractive power of the eye is insufficient to cause the light waves to form new centres at the retina; but if the refractive power of the eye be suitably increased by the aid of a positive lens placed between it and the object, vision is rendered distinct with the increased apparent size. A lens so used is called a simple microscope and the ratio of the apparent diam eter of the object to that which it would have at the conventional distance of 10 inches is called the magnifying power of the miscroscope. Since nature presents us with innumerable ex amples of such microscopes in small drops of water, of transparent resins, etc., the phenom enon has doubtless been known since prehis toric times, and we have the best of reasons for believing that some of the artisans of antiquity employed magnifiers as aids in their work.