. On the anomalies of accommodation and refraction of the eye, witha preliminary essay on physiological dioptrics. 453 ASTIGMATISM. but of unequal eccentricity and of unequal radius of curvature (, I. c). The maximum and minimum of radius of curvature corre-spond to the principal sections which are carried through the long axis andone of the short axes, the maximum usually corresponding to the hori-zontal, the minimum to the vertical principal section. Now, to such, anellipsoid the theory of Sturm is applicable. That a focal space thus arises,and what form its perpendicular sections
. On the anomalies of accommodation and refraction of the eye, witha preliminary essay on physiological dioptrics. 453 ASTIGMATISM. but of unequal eccentricity and of unequal radius of curvature (, I. c). The maximum and minimum of radius of curvature corre-spond to the principal sections which are carried through the long axis andone of the short axes, the maximum usually corresponding to the hori-zontal, the minimum to the vertical principal section. Now, to such, anellipsoid the theory of Sturm is applicable. That a focal space thus arises,and what form its perpendicular sections have, is above conspicuously repre-sented (Fig. 151). I think it necessary hereto introduce a fuller explana-tion, after Helmholtz. In Fig. 151, let the line y b be an axis of the. -frf » —&- ellipsoid, in the prolongation of which at p is the point of light. Let theplane of the diagram be a principal section of the ellipsoid, so that a secondaxis g h lies in this plane. The normals of all points of an ellipsoidal plane,which are met by a principal section, lie likewise in the principal sectionof the ellipsoid. And as a refracted ray remains in the plane, in which itlay with the normal, so rays, incident in a principal section, also remainafter refraction, in the principal section. When therefore a ray from pfalls upon the point c, the refracted ray remains in the plane of the diagram(in which the ray and the plumbline da lie), and cuts the axis b g in one ofits points q. The refracted ray is thereby more accurately denned throughthe condition that 1^sin acq must be =s n sin p c d,wherein n signifies the coefficient of refraction. This condition is the sameas for symmetrical or rotation surfaces. The almost perpendicular raysincident at b have therefore a
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