. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . cos <£2 .••(ID ft From equations I and II there are obtained different values of /2 and /3corresponding to the same value of fx. This means that P is imagedastigmatically. This astigmatic difference is greater the larger theobliquity of the incident beam. The equations for a reflecting spherical surface, which are of valuein the deductions relative to the astigmatic errors of various zones ofthe cornea, can be deduced from I and II by substituting in them nn n2= — 1, i. e., #! <£,. Thus fo
. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . cos <£2 .••(ID ft From equations I and II there are obtained different values of /2 and /3corresponding to the same value of fx. This means that P is imagedastigmatically. This astigmatic difference is greater the larger theobliquity of the incident beam. The equations for a reflecting spherical surface, which are of valuein the deductions relative to the astigmatic errors of various zones ofthe cornea, can be deduced from I and II by substituting in them nn n2= — 1, i. e., #! <£,. Thus for this case ?2. 2 cos^i ft 132 PHYSIOLOGICAL OPTICS 11 2 and = f! f3 r cos <&! and by subtraction, 112/1 v = — | cos ^ 1 f2 fa r \ cos $x / f3-f2 2or = — sin $x • tan <£x (Ill) f3f2 r 99. The interval of If a screen is placed near but behinda convex sphero-cylindrical lens, such for example as -f- 3 D. S. O + 3cyl. ax. 90, it will be found that the light from a small brilliant sourceof light at some distance in front of the lens (the writer uses a small. Lens. s Fig. 67.—The Interval of of diffusion and focal lines of a regularly astigmatic system. high candle-power incandescent lamp with frosted bulb at 20 feet)will be thrown as a luminous patch on the screen. If now the screenis withdrawn from the lens to a distance of cms., which is thefocal length of the combined sphere and cylinder, a vertical line willbe formed at Fly Fig. 67. As the screen is moved back still fartherfrom the lens this vertical line gradually changes into a prolate ovalat C, into a circle at B, into an oblate oval at A and finally into astraight horizontal line at F2. The screen is then at the distancecorresponding to the focal length of the sphere only; in the illustra-tion given it is at cms. The distance between the two foci, F1 andF2, of the two sharply defined lines is known as the astigmatic intervalor interval of Sturm. As the screen isi carri
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