. Carnegie Institution of Washington publication. THE AID OF THE ACHROMATIC FRINGES. 9 so that the sensitiveness is from (6), f x (7) w = — »(AAO = (a) It will next be desirable to deduce the above fundamental equations more rigorously than has thus far been done. Figure 2 is supplied for this purpose, and represents the more sensitive case where, in addition to the mirrors MM,' NN' (all but M being necessarily half-silvers), there is an auxiliary mirror, mm, capable of rotation (angle a) about a vertical axis a. The mirrors, M ---- N', in their original position, are conveniently at 45° to th
. Carnegie Institution of Washington publication. THE AID OF THE ACHROMATIC FRINGES. 9 so that the sensitiveness is from (6), f x (7) w = — »(AAO = (a) It will next be desirable to deduce the above fundamental equations more rigorously than has thus far been done. Figure 2 is supplied for this purpose, and represents the more sensitive case where, in addition to the mirrors MM,' NN' (all but M being necessarily half-silvers), there is an auxiliary mirror, mm, capable of rotation (angle a) about a vertical axis a. The mirrors, M ---- N', in their original position, are conveniently at 45° to the rays of light, while mm is <m'm normal to them. Light arriving at L is thus separated by the half-silver Af at i, into the two components i, 2, i, 9, 3, T and i, 6, 7, 6, 3, T, interfering in the telescope at T. When mm is rotated over a small angle a, these paths are modified to i, 2, 2', 4, 4', 5, T2 and i, 6, 7, 8', ™ 2 C" 4~ TI and T2 enter the telescope in parallel and produce interferences visible in the principal focal plane, provided the rays TI and T2 are not too far apart, in practice not more than i or 2 mm. Inter- ference fringes therefore will always disappear if the angle a is excessive, but the limits are adequately wide for all purposes. The essential constants of the apparatus are to be: (9, i) = (6, 3)=& (i, 2) = (6, 7)=C (9, 3) = (i, 6) = (2, 7)-* * .R being the radius of rotation. Where the mirror mm is rotated to m'm' over the angle a the new upper path will be: C+R tan. where (2' 4)=^, (4, 4')=^, (4/5)=g, the plane (8, 5) =5 normal to 7"i, and TZ being the final wave-front. The lower path is similarly 2 R + (C-R tan a)+d' to the same wave-front (8, 5), where (?', 8)=d'. Hence (apart from glass paths, which are preferably treated separately) the path-difference n\ (n being the order of interference) should be n\ = 2 R (tan a— i)-\-d-d'-\-e +g The figure, in view of the laws of reflection, then gives us in succession d =(b-\-c-\-R
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