Page:The American Cyclopædia (1879) Volume XII.djvu/671

OPTICS 657 it which fall on the mirror will proceed out- ward in parallel lines. This last mentioned property of paraboloid mirrors is applied in their use as reflectors on locomotives, and in lighthouses. But a large fraction of the rays emanating from the light at the focus of the FIG. 9. paraboloid do not strike the mirror, and there- fore diverge and are not useful in illuminating distant objects. To render these diverging rays parallel to the axis of the mirror, Thomas Stevenson, engineer of the English board of northern lighthouses, devised in 1834 the in- genious plan of placing a lens, L, fig. 9, before the mirror, to intercept the cone of rays, M/N, which is usually lost by divergence. Opposite this lens is a portion of the mirror, a 5, which is not paraboloidal but spherical, and the prin- cipal focus of the spherical mirror and of the lens is aty. By this simple device the cones of rays a fit and M/IsT are brought into a beam of parallel rays, R S, which proceed in the same direction as the rays reflected by the parabo- loid. Thus all of the rays are available, and from this property of these instruments they have been termed holophotal reflectors (Gr. SAo?, entire, and <j>&c, light). The object before a common concave mirror being anywhere without the centre of curvature, the image is between such centre and the focus, inverted, real, and reduced in size; and the places of object and image are interchangeable the foci are "conjugate," i. e., mutual. When the ob- ject is brought within the principal focus, the image is erect, virtual (behind the mirror), and magnified. The image with convex mirrors is always virtual, diminished, nearer the mir- ror than the object, and erect. II. DIOPTRICS. When a ray or a minute beam of light passes through any surface of division, separating vacuum from any medium, or any one medi- um from another of different density, a portion of the light is reflected at such surface, and an- other portion, never the whole, is transmitted. This transmitted light is always bent out of its course at the surface of division, never within the medium, if this be homogeneous ; and the light is then said to be refracted. If the medium be one of varying density, like the atmosphere, the ray is bent continually with- in it ; but this case is equivalent to its pass- ing through a succession of surfaces, dividing media more and more or less and less dense. Suppose a ray or minute beam of light trans- mitted at a point through a plane dividing surface, M N, fig. 10, between space and a medium, or any two media, and coming to such point in any direction whatever ; let fall to this point of transmission, O, a perpendicular to the surface, O P, and passing through it, so as to lie in both the media; then, first, it is universally true that the ray, after refraction, will be situated in the same plane in space in which this perpendicular and the line of the ray before refraction are situated. Thus we may always determine within what plane, ver- tical to the refracting surface, to look for the ray after refraction. The angle I O P, included between the perpendicular line and the ray before refraction, is termed the angle of inci- dence, and may be represented by I ; that be- tween the same perpendicular on the other side of the surface and the line of the ray after refraction, R O D, is the angle of refraction, E. These angles, the media being of different den- sity, are never equal; nor have the angles themselves any direct ratio to each other. But if in the course of the ray before, and also after refraction, equal radii, O B, O K, measured from the point where the ray penetrates the surface, be taken, and from the extremities of these radii perpendiculars, B A and R S, be let fall on the perpendicular line already drawn, these latter perpendiculars, B A (or I' S') and R S, will be the sines of the angles in which they are respectively, i. e., the sines of the angles of incidence and refraction. For any two given media, no matter what the angle of incidence, the corresponding angle of refrac- tion is such that the ratio of the sines is always the same is a constant value. Thus, the fun- damental and universal law of refraction at plane surfaces is also simple, though the con-