If rays issuing from O (fig. 5) be concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small.
With a considerable aperture, the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the sine condition, sin u'1/sin u1=sin u'2/sin u2, holds for all rays reproducing the point O.
If the object point O is infinitely distant, u1 and u2 are to be replaced by pi and h2, the perpendicular heights of incidence; the sine condition then becomes sin u'1/h1 sin u'2/h2.
A system fulfilling this condition and free from spherical aberration is called aplanatic (Greek a-, privative, plann, a wandering).
This word was first used by Robert Blair (d. 1828), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration.
Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most (uncorrected) systems with the aperture.
With a considerable aperture, the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the sine condition, sin u'1/sin u1=sin u'2/sin u2, holds for all rays reproducing the point O.
If the object point O is infinitely distant, u1 and u2 are to be replaced by pi and h2, the perpendicular heights of incidence; the sine condition then becomes sin u'1/h1 sin u'2/h2.
A system fulfilling this condition and free from spherical aberration is called aplanatic (Greek a-, privative, plann, a wandering).
This word was first used by Robert Blair (d. 1828), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration.
Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most (uncorrected) systems with the aperture.
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