File:On the anomalies of accommodation and refraction of the eye, witha preliminary essay on physiological dioptrics (1864) (14783991715).jpg

Identifier: onanomaliesofacc00dond (find matches)
Title: On the anomalies of accommodation and refraction of the eye, witha preliminary essay on physiological dioptrics
Year: 1864 (1860s)
Authors: Donders, F. C. (Franciscus Cornelius), 1818-1889 Moore, translator., William Daniel New Sydenham Society
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Publisher: London : The New Sydenham Society
Contributing Library: Internet Archive
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t the surface h2 the ray c b passesthrough unrefracted, but b c undergoes a deviation = c ab = y2. Now, the deviation of rays, parallel to b c, increases on the surface hx,between b and c, regularly from zero to yx; on the surface h2) betweenb and c, from zero to y2. Between b c and V c, therefore, lies a ray parallelto both, which, at the two sides, at /^ and h2i has an equal deviation. It isevident that we shall have found this ray, if a e is parallel to a e, or, inother words, if the angle e a b is equal to e a b. For that purpose let usconsider the triangles ab e and abe: these have the side ab parallel to ab,a e parallel to a e, finally, b e parallel to b e, because both are perpendi-cular to the axis. They are consequently similar, and therefore b e : V e = a b : a b,but because ab has the same inclination, with respect to hi <p\, that abhas with respect to h2 <p2, we may write, b e : b e = ht 0, : h2 $2 = Fx : F2. NON-COINCIDENCE OF PRINCIPAL AND NODAL POINTS. 55 Fig. 34.
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56 DIOPTRICS OF THE EYE. Finally, because the three lines a b&c, e o ee and Jcxcb a are parallel,kx o : h2 o = e a : c c,and as e a = eb and c e = 6 e lcx o : 7i-_, o — b e : b e =. Fx . F2. The point o e!s therefore found, by dividing the distance kx h2 between thecentres of curvature of the tiro surfaces into two parts, proportional to Fxand jFY, or (compare 26 and 2d) to the focal distances Gx and G be-longing to kx and k2. This expression is the more general: it is applicable to all cases, andtherefore also in the case where n = n, for which above (VIII.) anotherexpression was found. Now, if the point o be known, the positions of the two nodal points Jcand Jc, the images of o (as well as that of the two principal points h and Jc,the images of s), are calculated according to the formula 3 c, as is pointed outin VIII. By construction Jc and h have already been ascertained in Fig. 34.The anterior nodal point Jc lies, namelj, where the ray a e, prolongedas a right line (dotted),

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