The London, Edinburgh and Dublin philosophical magazine and journal of science . « I -jj- + -jp- {1 - v) I +am{+^-asin*c°s*(l_£C08<fr) i. ~ oao) w \ u / a sin -dr cos ijr / a , \ ) t ^-T(1-^cost)j=o. â. J ± q sin cos 6(1 cos) a cos y I* °a(° u \ u I + ^sm^rcos + (l-^cos*)|. . (7) Equation (7) determines the aberration in the general determine the effect of this in practice, let us suppose thatwe are considering the spectrum of the first order, so that theretardation of the light coming from two consecutive lines isjust one wave-length ; and hence, if P be on the #th line fromA,
The London, Edinburgh and Dublin philosophical magazine and journal of science . « I -jj- + -jp- {1 - v) I +am{+^-asin*c°s*(l_£C08<fr) i. ~ oao) w \ u / a sin -dr cos ijr / a , \ ) t ^-T(1-^cost)j=o. â. J ± q sin cos 6(1 cos) a cos y I* °a(° u \ u I + ^sm^rcos + (l-^cos*)|. . (7) Equation (7) determines the aberration in the general determine the effect of this in practice, let us suppose thatwe are considering the spectrum of the first order, so that theretardation of the light coming from two consecutive lines isjust one wave-length ; and hence, if P be on the #th line fromA, and a- the distance between two lines, then the arc AP =k<r=ia(D, and n = k. Let us suppose, further, that the origin of light is at thecentre of curvature of the grating, so that u = a, = 0, andhence, taking the â ve sign in (6), sinyft= -, cos^=/y/ (l- ^V u=aco^=a^/(l - \ Thus JcX8M=+a cwhich is determined by w/=acos/^r, Q being the point on Fig. that line at which light arrives in exactly the same phase fromA and P. Then QiQ^&X. And the-angle PQaA differs by 418 Mr. R. T. Glazebrook on only a small quantity from o>; while, since QQi is small com-pared with PQ, the angle Q1PQ/ is small compared with , if QR be drawn at right angles to PQi, the light fromP arrives at R in the same phase as at Q/, and the differencein phase at QJl between the waves coming from A and P isQiQ â QiR= QiQ^l â cos a)) > an(i to the same approximationthis is equal to ^kXco2. So that if we consider as well the lightcoming from a point k lines below A, the extreme differenceof phase in the various waves which reach the point Qi is^(k + k)\co2; k + kf will be the total number of lines in thegrating. Thus in one of Prof. Rowlands gratings we have a = 213 centim., 37o,= 2^ about, k+k=14250; and hence the difference in phase is about 7X/10. Hence theaperture of the grating is too large to give the best defini-tion : for that purpose the
Size: 2446px × 1021px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
