OPTICAL DEFECTS OF THE EYE 523 



are perpendicular to each other, the astigmatism is described as regular. We 

 shall discuss only this kind of astigmatism here. 



An astigmatic beam may be formed in two ways: (1) When the optical 

 system is asymmetrical and the incident rays vertical; and (2) when the 

 optical system is symmetrical and the incident rays oblique. 



The first case is the simplest (for the second see page 525). Suppose we 

 have a lens, which in the horizontal meridian has a refractive power of 10 

 diopters; in the vertical meridian a refractive power of 12 diopters. It is 

 evident that the beam after refraction will no longer have a common focus, 

 for the incident rays in the horizontal meridian are brought to a focus 

 T V m. behind the lens and those falling in a vertical meridian ^ m. behind 

 the lens. 



Further study of the problem has shown that if no account be taken of 

 the spherical aberration, the light rays instead of being converged to foci 

 at the focal points of the two meridians are converged into a focal line per- 

 pendicular to the principal ray at each of those points. The first focal line 

 corresponds to the focal point of the meridian with the strongest refractive 

 power and is perpendicular to that meridian i. e., in the plane of the weakest 

 meridian. The second focal line corresponds to the focal point of the weakest 



FIG. 218. Illustrating spherical aberration. The rays parallel to the axis of the system are 

 converged to foci nearer and nearer the convex surface the farther they are removed from 

 the axis. 



meridian and is perpendicular to that meridian i. e., in the same plane as the 

 strongest meridian. 



In front of the first focal line the beam of rays forms in a cross section 

 an ellipse with the longer axis in the direction of the first focal line, beyond 

 the second focal line the beam forms an ellipse with the longer axis in the 

 direction of the second focal line. A transition from the one elongation 

 to the other takes place between the two focal lines, the upright ellipse 

 becoming first a circle and then a procumbent ellipse (Fig. 219). 



In an astigmatic eye, therefore, a homocentric * bundle of rays cannot be 

 brought to a single focus. When the eye is adjusted for the most refractive 

 meridian, the images on the retina are all drawn out in the direction of the 



1 That is, rays proceeding from a common point or rays which pass through a common 

 point when prolonged. 

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