. The London, Edinburgh and Dublin philosophical magazine and journal of science. the corresponding refracted rays in elevation by thelines ag and ag and in plan by the line ah. The tworefracted rays will intersect in the horizontal plane in thepoint h which is at the extremity of the tangential focal linecorresponding to the semi-aperture h2. If hg = gk = l2 and og = v2, we have from the triangles obe and ehg (fig. 2), i>2 —*>i or k = h^ay, . CO 6*2 Mr. A. Whitwell on the Lengths of th But v2 = fjbu and — — - = a( — — — Y By eliminating u we find v — ^^ ?2(yCt — 1)4 ^l and substituting
. The London, Edinburgh and Dublin philosophical magazine and journal of science. the corresponding refracted rays in elevation by thelines ag and ag and in plan by the line ah. The tworefracted rays will intersect in the horizontal plane in thepoint h which is at the extremity of the tangential focal linecorresponding to the semi-aperture h2. If hg = gk = l2 and og = v2, we have from the triangles obe and ehg (fig. 2), i>2 —*>i or k = h^ay, . CO 6*2 Mr. A. Whitwell on the Lengths of th But v2 = fjbu and — — - = a( — — — Y By eliminating u we find v — ^^ ?2(yCt — 1)4 ^l and substituting this value of t^ in (2) we get L = A or /,= /l that is the length of the tangential focal line = the tangential aperture x distance of the line from thesurface x power of the surface. 2. To find the lengths of the focal lines of asphero-cylindrical lens. Figs. 3 and 4 represent an elevation and a plan of theincident and refracted rays at the second or spherical surface,the corresponding rays at the first or cylindrical surfacebeing represented in figs. 1 and Let q q be the centre of the spherical surface the radius of which = —r2. (a) The axial focal line. The two symmetrical rays, represented in elevation by theline af\ which were the refracted rays at the cylindricalsurface, are now the incident rays. After being refracted at Focal Lines of Cylindrical Lenses. 63 the spherical surface they will intersect at the point n onthe line joining the point/ to the centre qf of the sphericalsurface. The point n is at the extremity of the axialfocal line. If m!n! = l3 and om = vB we have from the trianglesfeq and nmq (fig. 3), ^3 — ^2 or L = L (3) From the ordinary formula for spherical lenseswe have pWs (//,— i)t78+r2 and substituting this value o£ vi in (3) we get or the length of the axial focal line of a sphero-cylindricallens = axial aperture X distance of the line from the lensx the glass to air power of the cylindrical surface. —-— = the glass to ai
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
