RECTILINEAR PROPARATION. A point-source of waves produces a spherical wave-front in an iso tropic medium, because the velocity is the same in all directions. Let 0 be such a point-source of waves; NM the section by the paper of the spherical wave-front at any instant; P is some point in front of the wave-front Si is the inter section of the wave-front by the line OP. When it is said that light travels in a straight line. it is equivalent to saying that. if an opaque ob stacle is placed with its edge at the point M, its shadow will just include P. It can be shown that the principle of Huygens predicts that this statement is not quite accurate; and more care ful experiments prove that the modifications sug gested are observed. Instead of considering all the infinite spherical secondary waves, proceed ing from the surface NM to P. the disturbances may be grouped together according to a manner devised by Fresnel. Call the distance PAI a, and let the wave-length of the waves be X: then with P a. a centre draw spherical surfaces of radii a :5, a + a etc. These surfaces will intersect the spherical wave-front in circles which will thus include zones between them. the distinguishing characteristic of a zone being that any point in it lies at such a distance from P that there are points in the two contiguous zones for which the distances to P differ from it by half a wave-length. Consequently, if the continued effect of the action of all the secondary waves from the points of any one zone is to pro duce action in one direction. the resultant action due to both the neighboring zones is in the op posite direction. Let the numerical values of the effects at P due to the different zones be In, ni„ etc., for the first or central zone around M, the second, third, etc. The final nu merieal value of the action of the secondary waves is. therefore, Ill y — Ili, + Ill a — + — etc.
The value of on for any zone depends upon three things: the area of the zone, the distance of the zone from P. and the inclination of the line join ing P to the zone with the line P.110. It may he shown that owing to these causes the value of M for any zone is less than that for the one just inside; and, if the wave-length is small, as it is in the case of ether-waves (and also for the waves produced in air by very shrill sounds), this difference between the numerical values of the action for the zones is small. Under these con ditions the above sum — m. + w, — etc.,
duces to simply .1711. In words, the action at 1' owing to the secondary waves from any olle zone is neutralized by that of the waves iron: one half of each of the neighboring zones; and so the final action at I' is one-half of that due to the secondary waves from the central zone around M. If the wave-length is extremely small, as in ether-waves, the areas of these zones are almost infinitesimal; but if the wave length is long, as in aerial waves, they have a sensible size. If the action of the central zone is blotted out by an opaque obstacle. the action at P due to the rest of the wave-front spreading out from t he source at 0 is etc., or .1m,, and is therefore hardly changed at all, if the ZWICs are small. if tile obstacle blots out two zones, the action at 1' is etc. Consequently, if any small eiren lar opaque disk is placed at Al at right angles to the radius. there is always action at P, and its value is one-half that due to the first zone outside the edge of the disk. Naturally as a larger and larger disk is used the intensity of the action at P decreases. Similarly, if an opaque screen with a circular opening is placed at M. the effect at P depends upon the area of the open ing. if this area is that of the first zone, the action at P is twice what it would be if the screen were entirely removed; if the area in eludes two zones, there is practically no action at I'; etc.
If the opaque screen has zonal openings so as to expose only the odd zones, the effect at P is + m, + etc., and so is very intense. .1f this 'zone-plate.' so called. is modified so that the opaque rings are replaced by transparent rings of such a thickness as to introduce a dif ference of half a wave-length by virtue of the fact that the velocity of light in the transparent ma terial is less than in air, all the zones will con spire to help in the action at I'. it is evident that the size of the zones varies with the color of the light; and if white light—or a mixture of colors—is corning from the source, passing either through a small circular opening or around a small circular disk, there will he colored near P. All of these effects with openings and disks are amply verified by experiments with both ether and aerial waves. the only difference com ing from the fact that the aerial waves are as a rule many centimeters long. while the ones in the ether that affect our sense of sight have a length of about 0.00005 of a centimeter.