The London, Edinburgh and Dublin philosophical magazine and journal of science . while theother spreads out into the medium containing the incidentwave. The reinforcement of the wavelets propagated in themedium containing the incident wave gives rise to thereflected wave-front. The wavelets propagated in the mediumbeyond the interface may or may not be able to reinforceeach other, with the result that a refracted wave may or maynot be formed, according to circumstances. If no refractedwave is formed, the secondary wavelets in the mediumbeyond the interface destructively interfere with each oth
The London, Edinburgh and Dublin philosophical magazine and journal of science . while theother spreads out into the medium containing the incidentwave. The reinforcement of the wavelets propagated in themedium containing the incident wave gives rise to thereflected wave-front. The wavelets propagated in the mediumbeyond the interface may or may not be able to reinforceeach other, with the result that a refracted wave may or maynot be formed, according to circumstances. If no refractedwave is formed, the secondary wavelets in the mediumbeyond the interface destructively interfere with each otherthroughout that medium ; but in all cases secondary waveletsare formed in each of the media separated by the interface. 2 A2 348 Messrs. Edser and Senior on the Diffraction of Let AC (fig. 1) be a plane surface o£ separation betweentwo media, of which the lower is the denser ; and let AB bethe trace of one of a series of plane waves, incident in thedirection BC on the surface. In order that there should bea resultant disturbance at P, a point in the upper medium, Fie-. wavelets originating in the immediate neighbourhood ofsome point A must reach P in the same phase. Let NAN7be the normal to the surface at A. Then if i is the angle ofincidence, this will be equal to the angle BAC which theincident wave makes with the surface AC. Let the anglePAN be equal to 6, and let the upper medium be the freeaether, while the refractive index of the lower medium isequal to fi. Then in order that wavelets from A and E. twoneighbouring points on the surface AC, should reach P inthe same phase, we must have AP = /*.DE + EP, (1) where DE is the perpendicular distance of the point E fromthe plane wave AB. Let AP = d, while AE = 8. Then (EP)2 = d2-f-S2-2^sin0 DE = Ssin/, d=(d2 + S2 - 2dS sin 6)^ + ^8 sin i, and from (1), .. sin 6=/j, sin i — ^-, (fx2 sin2 i — 1), (2) If S is of very small magnitude, and the point P is at anappreciable distance from A, d will be very great in com-parison
Size: 1785px × 1400px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
