OPTICS. The study of Optics is usually divided into three parts: Physical Optics, Physiological Optics and Geometrical Optics. Physical Optics is primarily concerned with the nature and prop erties of light itself and is treated under LIGHT. Physiological Optics deals with the mechanism of vision, and is treated under VISION.
Geometrical Optics, which is the subject of this article, is the name applied to that part of Optics which deals with the prop erties of optical instruments such as telescopes, microscopes, photographic lenses, spectroscopes and the elementary lenses, mirrors and prisms from which they are constructed. As geo metrical methods have been widely employed in inquiries con cerning optical instruments, the name is not without historical justification. Nevertheless we shall have occasion to take excep tion to the validity of these methods in this field. They are in fact only admissible to an extent which deprives the historical theory of much of its utility. A brief account of this theory can, however, hardly be omitted here both on account of its historical importance and because even at the present day the majority of the literature on the subject is still couched in geometrical terms.
The basic conception of geometrical optics in this theory is the ray of light. The fact that light travels in straight paths was well known to the Greek mathematicians and the transition from op tics to pure geometry was thus simple. More precisely in geo metrical optics we assume that the ray of light continues in the same straight line while it travels in the same homogeneous me dium. When it encounters a surface separating this medium from another, for example the surface between air and water, the ray proceeds in another direction from the point in which it meets this surface, and again continues to follow a straight path until another surface is reached. The new path may be in either the original or the new medium. In the former event the ray is said to be reflected, and in the latter refracted, at the surface of sepa ration. We regard the whole continuous path of the light as a single ray, but distinguish the original and final portions as the incident ray and the emergent ray respectively. We may also
apply the terms reflected ray or refracted ray as the case may be to the latter.
The new directions are determined by simple geometrical laws. The law of reflection states (1) the incident ray, the reflected ray, and the normal to the surface at the point of reflection lie in one plane; (2) the incident and reflected rays lie on opposite sides of the normal (3) the angles made by the incident and reflected rays with the normal are equal. The law of refraction states (I) the incident ray, the refracted ray, and the normal to the surface at the point of refraction lie in the same plane; (2) the incident ray and the refracted ray lie on opposite sides of the normal ; (3) the sine of the angle made by the incident ray with the normal bears a constant ratio to the sine of the angle made by the re fracted ray with the normal. This ratio depends only on the corn position of the two media separated by the surface, and is known as the relative index of refraction.
From a comparison of these two laws it will be seen that the law of reflection may be considered as a special case of the law of refraction, the relative refractive index being equal to either + I or — 1. Let us adopt the convention that angles are to be measured by the value of the anti-clockwise rotation needed to reach the ray position from the onward drawn normal. Thus in fig. Ia, the angles of incidence and refraction 4 and (/)/ are posi tive, and if A is the relative refractive index sin4= ,u sin4'. When reflection occurs the angle of reflection is opposed in sign to the angle of incidence (see fig. 1, right), and is should therefore receive the value — I. It will be noted also that the reflected ray travels in the opposite direction to that contemplated in the law of refraction. As we shall see later all lengths entering into optical equations are either multiplied or divided by a refractive index and the double reversal of sign frees us from all difficulties regard ing the signs of the quantities we employ. We are therefore enabled to dispense with any detailed consideration of reflecting instruments and can proceed to deal with refraction as an in clusive process.