The London, Edinburgh and Dublin philosophical magazine and journal of science . 422 + -0364 + -2183 + 456 + -0218 + 4419 + -101 •0000 •0000 •000 tensity as if the apertures were self-luminous. The annexedtable gives the numerical values required. -In cases (i.) and(iii.) the resultant amplitude is symmetrical with respect tothe point u=~\tt midway between the two geometricalimages ; in case (ii.) the sign is reversed, but this of coursehas no effect upon the intensity. Graphs of the three functionsare given in fig. 4_, the geometrical images being at thepoints marked —u and
The London, Edinburgh and Dublin philosophical magazine and journal of science . 422 + -0364 + -2183 + 456 + -0218 + 4419 + -101 •0000 •0000 •000 tensity as if the apertures were self-luminous. The annexedtable gives the numerical values required. -In cases (i.) and(iii.) the resultant amplitude is symmetrical with respect tothe point u=~\tt midway between the two geometricalimages ; in case (ii.) the sign is reversed, but this of coursehas no effect upon the intensity. Graphs of the three functionsare given in fig. 4_, the geometrical images being at thepoints marked —u and 0. It will be seen that while in caseiii., relating to self-luminous points or lines, there is anapproach to separation, nothing but an accurate comparisonwith the curve due to a single source would reveal theduplicity in case i. On the other hand, in case ii., where * Phil. Mag. vol. viii. p. 266, 1879. ivith Special Reference to the Microscope. 179 there is a phase-difference of half a period between theradiations, the separation may be regarded as complete. Fig. In a certain sense the last conclusion remains undisturbedeven when the double point is still closer, and also when theaperture is of any other symmetrical form, e. g. at the point of symmetry in the image, midway betweenthe two geometrical images of the radiant points, the com-ponent amplitudes are necessarily equal in numerical valueand opposite in sign, so that the resultant amplitude or illu-mination vanishes. For example, suppose that the apertureis rectangular and that the points or lines are twice as closeas before, the geometrical images being situated at u= — ^7r,?^ = 0. The resultant amplitude is represented by /(w),where sin u sin {u 4- \tt) /(«)= U + ^TT (17) The values of f(u) are given in Table III. They show-that the resultant vanishes at the place of symmetry ?/ = K 180 Lord Rayleigh on the Theory of Optical Images, and rises to a maximum at a point near u = ^7r, considerab
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