THE SENSES 



893 



Reflection from a Concave Spherical Mirror. A spherical surface 

 may be supposed to be made up of an infinite number of infinitely 

 small plane surfaces. The normal to each of these plane surfaces 

 is the radius of the sphere, and the reflected ray makes with the 

 radius at the point of incidence the same angle as the incident rav. 

 Let D (Fig. 370) be the middle point of the mirror, and C its centre 



FIG. 370. REFLECTION FROM A CONCAVE FIG. 37.1. FORMATION OF REAL IN- 

 SPHERICAL MIRROR. VERTED IMAGE BY A CONCAVE 



SPHERICAL MIRROR. 



of curvature i.e., the centre of the sphere of which it is a segment. 

 Then CD is the principal axis, and any other line through C which 

 cuts the mirror is a secondary axis. When the mirror is a small 

 portion of a sphere, rays parallel to the principal axis are focussed 

 at the principal focus F midway between C and D ; rays parallel to 

 any secondary axis are focussed in a point lying on that axis ; and 

 rays diverging from 

 a point on any axis 

 are focussed in a point 

 on the same axis. 



These facts afford a 

 simple construction 

 for finding the posi- 

 tion of the image of an 

 object formed by a 

 concave mirror. Let 

 AB be the object 

 (Fig. 371). Then the 

 image of A is the 

 point in which all 

 rays proceeding from 

 A and falling on the 

 mirror, including rays 

 parallel to the princi- 

 pal axis, are focussed. 

 But the ray AE, 

 parallel to the principal axis, passes after reflection through the 

 principal focus F, therefore the image of A must lie on the straight 

 line EF. If any secondary axis ACD be drawn, the image of A must 

 lie on ACD. It must therefore be the point of intersection, a, of EF 

 and ACD. Similarly, the image of B must be the point of intersec- 

 tion, b, of GF and BCH. The image ab of an object AB farther 



FIG. 372. FORMATION OF IMAGE BY A CONVEX 

 MIRROR. 



