If the point m be situated near the geometrical projection of the boundary of the aperture, whether Inside or outride, or if the spar tare be so small that a few only of the spheres above mentioned cut it, the determination of the disturbance at at becomes a more difficult problem, and belongs to diffraction. The explanation of the exist ence of rays and shadows when the light is divergent, or the inter cepting screen is not perpendicular to its course, is nearly the same as before.
We come now to the colours of thin plates, one of the first phe nomena to the explanation of which the principle of interference was applied. A., however, the whole subject has been referred to the present article, we shall commence with a description of the pheno menon itself, and of its laws, as discovered by Newton. The colour.
of thin transparent lamina had previously been studied to a certain extent, by Boyle and by Hooke, and the latter of these philosophers produced the phenomena in the instructive form in which their laws have since been studied, namely, by placing two objecteglaeses in contact. It was in this form chiefly that they were studied by Newton, and from him the coloured rings formed by such glasses have been called Newton', rings.
In order to observe these rings conveniently, Newton placed two convex lensed of long foci (14 and 50 feet) in contact with each other at their vertices, keeping them together by means of three clamps at intervals on their circumferences, so that there was between them a i.ery thin plate of air, concave on its upper and lower tides. On bring ing the pair of lenses to an open window, and receiving the rays of light from the sky by reflection from them, there were observed, the plates being gently pressed together, seven series of coloured rings or bands about a black spot in the centre : beyond the seventh band the colours could scarcely be distinguished. The diameters of the hands being measured, where the colour in each was the brightest, Newton found that those diameters were proportional to the square roots of the series of odd numbers 1, 3, 5, 7, &c.; at the places where the colours were the least bright, the diameters were found to be propor tional to the square roots of the series of even nnmbers 2, 4, 6, 8, fic.
The radii of curvature of the lenses being known, Newton com puted the thicknesses of the plate of air at the circumferences in which the colours of the bands had the greatest and least degrees of brightness ; and he found ('Optices; lib. ii) that, at the most luminous part of tho ring nearest to the centre, the thickness was equal to inch ; the thickness at the most obscure part of that ring was equal to inch. Hence, from the law above mentioned, the
thicknesses of the air at. the most and ]cast luminous parts of the suc ceeding rings may be obtained; those thicknesses being considered as proportional to the squares of the semidiameters of the rings.
If lenses whose surfaces have difkrent curvatures are employed, it is always found that like tints are produced in the circumferences of circles at places where the intervals between the surfaces arc equal, the eye being similarly situated, or a line supposed to be drawn to it from the centre making equal angles with a plane passing through all the rings; and this circumstance serves P3 show that the tints depend wholly on the distances between the lenses. If the angle made by the line drawn to the eye be diminished, the diameters of the rings will be increased, the tints remaining the same. Newton found that for moderato obliquities the sarne ring was formed where the distance between the lenses, or the thickness of the interposed plate of air, varied as the secant of the angle of incidence on the first surface of the lens, which in estimating this angle may ho deemed a plate bounded by parallel surfaces. To include great obliquities he has given an empirical rule not sensibly differing from the simple rule of the secant except at great obliquities: It has since, however, been found by careful measures of the diameters of the rings at great obliquities, that the thickness where a given ring is formed is regulated by the simple law of the secant, and not by the more complicated formula given by Newton.
When the rings are formed by homogeneous light they are found to he more numerous than when the light is mixed, indeed they are almost countless when the homogeneity is sufficiently perfect; they are also of the same colour as the light, and are separated from one another by narrow spaces which are quite black. The diameters of the rings in the corresponding bands, at the place ll whore the colours arc the brightest, are different when the bands are formed by homogeneous lights of different colours, being least when the light is violet, and greatest when red ; and Newton computed, from the measured diameters of the rings of different colours, the intervals between the lenses at the places where the brightest parts of the first rings from the centre are formed : these distances arc found to be equal to inch for extreme red rays, and inch for extreme violet rays, which it may be observed are half the lengths of an undulation for those kinds of light.