INTRODUCTION TO PHYSIOLOGICAL OPTICS 427 



= C E G, and C G E is an isosceles triangle. Then 

 if r be the radius and x the angle formed by the 

 perpendicular C E with the axial ray C G, CG 



T 



. So long as angle x is small, cosine x 



2 cos x 



will be nearly 1. C G will then be nearly one 

 half the radius OK. Hence incident rays near 

 the axial ray C'K will be reflected approximately 

 to the principal focus F, which lies half way 

 between the centre of curvature and the mirror. 

 As the aperture 1 of the mirror increases, angle x 

 also increases. The larger x, the smaller will l;e 

 the denominator of the expression for G G, and the 

 greater the distance of G from C. Kays reflected 

 from the outer portion of a mirror of larger aper- 

 ture meet the principal axis nearer the mirror 

 than those reflected from the central portion. 

 The intersection of the reflected rays produces a 

 curved line the caustic curve or focal line. By 

 revolving Fig. 2 about the axis C K, a caustic or 

 focal surface will be obtained. 2 



Spherical Aberration by Refraction. 1. The 

 observations just made concerning concave mir- 

 rors are applicable also to lenses. Eays entering 



1 The aperture is the angle included between lines drawn 

 from the principal focus to the margins of the mirror or lens. 



2 Jochmann and Hermes. Grundriss der Experimental- 

 physik, 1890, p. 153. 



