PHYSIOLOGICAL OPTICS 797 



principal axis of this reflecting surface. Any other line passing 

 through C to a different point of the mirror than its middle, consti- 

 tutes a secondary axis. The perpendicular of each of the small planes 

 forming this reflecting surface, is the radius of the sphere and each 

 reflected ray forms with the corresponding radius the same angle as 

 the incident ray. Thus, all rays parallel to the principal, axis (AB and 

 EH, Fig. 405) are brought to a focus at the principal focus F midway 

 between C and D. Quite similarly, all rays pursuing a course parallel 

 to any secondary axis, are brought to a focus in a point lying on this 

 axis. Hence, if the principal focus F were converted into a luminous 

 point, the rays emitted from here would be reflected back into rays 

 taking their course parallel to the principal axis. 



If the luminous point L is situated upon the principal axis at a distance insuffi- 

 cient to render the rays emitted by it parallel, then the divergent incident ray LB 

 (Fig. 406) and the perpendicular BC form the angle LBC. This angle is smaller 

 than that formed by the parallel ray AB with the corresponding normal BC', and 

 hence, it may be inferred that the angle of reflection of a divergent ray is smaller 

 than the angle of reflection of a parallel ray. Consequently, the principal focus 

 of L must lie in L 1 between F and C; i.e., between the center of curvature and the 



FIG. 406. REFLECTION FROM A CONCAVE SPHERICAL MIRHOR IF ITS INCIDENT RAY is 



DIVERGENT. 



principal focus F. By converting L 1 into a luminous point, the rays may in the 

 same manner be reflected outward into L. The latter, therefore, may be said to 

 be the conjugate focus of L 1 . It will then be seen that if the luminous point L is 

 placed in the center C, the angle of incidence is null and the angle of reflection null. 

 Consequently, the ray is reflected upon itself so that its focal point coincides with 

 the luminous point. Lastly, if the luminous point L is situated between the center 

 of rotation C and the principal focus F, the conjugate focus must be on the other 

 side of the center and the farther from it, the shorter the distance between L and 

 the principal focus. These principles find their application in the explanation of 

 Purkinje's image reflected from the concave anterior surface of the vitreous humor. 



The reflection from convex spherical surfaces finds its application in the images 

 formed upon the anterior surfaces of the cornea and lens. Supposing that the 

 entering ray pursues a course parallel to the principal axis of the convex mirror, 

 its reflection from the latter will give to it a divergent course. If the reflected ray 

 is continued by an imaginary line through the mirror, it will be seen to strike the 

 principal focus at F which is approximately the center of the radius of curvature 

 CD of this mirror. 



The images formed by rays of light differ with the direction assumed by them 

 after their reflection. When they converge, as after their reflection by concave 

 mirrors, they form a real image in front of the mirror and on the same side as the 



