Page:Elementary Text-book of Physics (Anthony, 1897).djvu/423

§ 336] spherical surface. It is a concave mirror if reflection occur on the concave or inner surface; a convex mirror if it occur on the convex surface. The centre of the sphere of which the mirror forms a part is its centre of curvature. The middle point of the surface of the mirror is the vertex. A line through the centre of curvature and the vertex is the principal axis. Any other line through the centre of curvature is a secondary axis. The angle between radii drawn to the edge of the mirror on opposite sides of the vertex is the aperture. To investigate the effects of reflection from a spherical surface, let us consider first a concave mirror. Let a light-wave emanate from a point $$L$$ on the principal axis (Fig. 101). In general, different points of the wave will reach the mirror successively, and, considering the elementary waves that proceed in turn from its several points, the reflected wave surface may be constructed as for a plane mirror. If the mirror were not there the wave front would, at a certain time, occupy the position $$aa.$$ Drawing the elementary wave surfaces we have $$bb,$$ the position at that instant of the reflected wave. Its form suggests that of a spherical surface, concave toward the front, and having a centre at some point on the axis. The elementary waves at $$B$$ will certainly send light to some point $$l$$ on the axis. We will examine the conditions which must be fulfilled in order that