GEOMETRICAL OPTICS. Fundamen tal The fundamental characteristics of the mode of propagation of light in so called isotropic media are usually explained in terms of three propositions, namely, (1) the law of the rectilinear propagation of light,(2) the mutual independence of the "rays)) which constitute a beam of light, and (3) the abrupt changes in the directions of the rays of light produced by reflection or refraction at a sur face of separation between two media of dif ferent optical densities like air and glass. These laws (which are to be regarded as only partially exact) are concerned essentially with the directions which the light pursues under given conditions and are therefore purely geometrical; and hence the science which is based upon them and which seeks by their aid to explain the phenomena of light, either as they occur in nature or as they are produced by the agency of optical instruments, is called Geometrical Optics.
The fact that light traverses a homogeneous medium in straight lines is confidently assumed in matters of everyday life, although it is known to be not absolutely and unexceptionally true. When an opaque body is interposed any where in the straight line joining a luminous object with the eye, the object is thereby ren dered invisible, and the familiar phenomena of shadows find their simplest explanation in this law. The principle of the mutual independence of the rays of light assumes that each ray in a beam of light is somehow separate and distinct from its fellows and has therefore a certain physical existence, although it is impossible to isolate a single ray of light. Actually, we have always to deal with a bundle of rays, which may be homocentric or monocentric (in case all the rays of the bundle meet in one point), but which, in general, is astigmatic (which means literally °without focus"). The laws of the re flection and refraction of light remain to be stated.
When light is incident on a smooth, polished surface separating two isotropic media of dif ferent optical densities, part of the light will be reflected back into the first medium and part will be refracted into the second medium, ac cording to the following laws: (1) Both the reflected and refracted rays lie in the plane of incidence (which is the plane determined by the incident ray and the normal to the boundary-surface at the point of in cidence: see Fig. 1).
(2) The angles of incidence (a) and re flection (p) are equal in magnitude but op posite in sign (p--- —a); that is, the incident and reflected rays lie at equal angular distances from the normal on opposite sides thereof (Law of Reflection).
(3) The sines of the angles of incidence (a) and refraction (a') are in a constant ratio, which is equal to the ratio of the ties of light (v, v') in the two media; that is, sin a : sin constant.
The value of this constant depends only on the nature of the two media and the color of the light or its wave-length in vacuo. (Law of Re fraction).
By the angles of incidence, reflection and re fraction are meant here the acute angles be tween the incidence-normal and tLe incident, reflected and refracted rays, respectively.
This constant ratio of the velocities of propagation of monochromatic light in two different media is called the relative index of refraction of the two media. The absolute index of refraction of an optical medium for a given kind of light is defined to be the ratio of the velocity of light in vacua to its velocity in the medium in question. If the absolute in dices of refraction of two media are denoted by n and n' then v:v'°n':n, and, accordingly, the law of refraction may be written in the following invariant form: n • sin a=.--n' ' sin a'.
Since the velocity of light in a is different for light of different colors, the index of refraction of a medium depends on the color of the light, and hence in speaking of the index of refraction of a substance it is neces sary to specify the quality of the homogeneous or monochromatic light to which this number refers. Usually its value is found to be greater for yellow light than for red and greater for blue than for yellow; so that, in general (al though there are some curious exceptions), light is found to be more and more "re frangible" as we proceed from the red to the violet end of the normal spectrum. When we say, for example, that the index of refraction of water is 1.334 or that of alcohol is 1.363, generally it is tacitly assumed that the value ap plies to rays of light corresponding to the Fraunhofer D-line in the light yellow part of the solar spectrum, which is characteristic of the light emitted by incandescent sodium vapor. Thus, of yellow light in vacua ng— velocity of yellow light in the given medium The indices of refraction of the more useful kinds of glass used for optical prisms and lenses vary from about nD =1.49 to n D== 1.65. The index of refraction of air at Oic• and under a pressure of 76 cm. of mercury is "D...* 1.0002429, which is so nearly equal to unity that it is usually so considered.