LIGHT. 246 LIGHT. grazing its boundary form what is called the ■geonu'trical shadow.' Tims if OMP is one of these rays, the shadow lies on one side of it. The elicct at a point (.} just within the shadow can be found by considering the zones on the wave-front around X. which correspond to Q. It is evident that there is an action at Q due to those zones which are not obscured by the ob- stacle. As points are taken farther and farther in the shadow, however, this efl'ect becomes less and less, gradually fading away. (This explains why aerial waves pass around corners into the 'shadow,' and asserts the same phenomena for ether-waves, only to a mucli less distiince, owing to the smallness of the zones in their case. This is actually observed.) Similarly, the action at <a point R outside the shadow depends upon the number of zones drawn around S. the intersection of OR with the wave- front, which are not obscured by the opaque ob- stacle. If R is v<'r}' close to P, only the first zone may be uncovered, and the action is intense: but as R recedes from P the second zone liegins to neutralize the action of the first, and so the in- tensity at R decreases; then, as R continues to recede, the action again increases, etc., until R is .so far away from P that the action of the zones of high order makes no difference. Conse- quently, if homogeneous light is used, and a screen is placed to receive the shadow, there will be no sharp shadow, but the light will gi-adually fade away in the geometrical shadow, while out- side this shadow there will be bright and dark hands following the general shape of the obstacle. These phenomena can be easily observed. If white light is used, these rings will be colored, because their position depends ujion the wave-length and so each color will have its own set of rings; biit at a comparatively short distance from the edge of the geometrical shadow the effect is a uniform white illumination. These bands are called 'dif- fraction' bands; and the whole phenomenon is said to be due to 'diffraction' (q.v.), as is also that of the small disks and openings. These diffraction rings or bands are seen most clearly if the opaque obstacle has a linear edge like a knife edge and if it is illuminated by light coming through a slit parallel to this edge: then, if the light is received on a screen suitably placed, the bands will be most distinct. Other cases of diffraction will be discussed later. It thus appears that the sense in which light travels in straight lines is not in the casting of sharp shadows, for it does not. but in the fact that as ether-waves spread out from a point- source O. (here being no obstacles, the effect at a point P is due entirely to the action of a minute portion of the wave-front around M where the ray OP intersects it. Laws of Reflection. It is not difficult to show that the laws of rellection are a direct Fig. 15. ABC to represent the section of a plane by tin paper, and similarly the line A'C'R", niakin,. the angles CAA' and C'A'A eipial; draw the lines CC and UB' perjK^ndieular to the plane ABC and the lines C'C" and B'B" perpendicular to the plane A'C'B"; draw also B'P perpendicu- lar to CC and C'Q perpendicular to B'lJ". if the plane A'C'B" represents a wave-front reced- ing from the plane surface AB'CA, the actions at B" and C" are entirely due to those that were at B' and C a short time previously; similarly, if the plane ABC represents an advancing wave- front, the actions at B' and C will be due to lho.se now at the points B and C. Therefore if the time taken for the disturbance to pass from B to B' to B" is the same as it is for the dis- turbance to pass from C to C to C", the receding wave-front is due to the reflection at the surface AB'CA' of a wave-front which was at ABC some time previously. But these times are the same because the lengths of the lines CC'C" and BB'B" are evidently cqvial by geometry, and the me- divim in which the distiirbances are traveling is the same for both. Consequently, the ray BB' is reflected into the ray B'B" ; they make equal angles with a line drawn perpendicular to the surface at B' and these lines lie in one jdane. Laws of Refraction. In a similar manner the laws of refraction may be deduced. Let AB'CA' be the intersection of the paper with a plane surface separating two transparent media; let ABC represent the section of the consequence of the principle of the rectilinear propagation of light. Let AB'CA' be the section of a plane surface by the paper; draw the line Fig. 16. paper willi a plane in one medium, and A'C'B" with a plane in the lower medium ; draw BB' and CC perpendicular to the former and B'B" and CC" perpendicular to the latter, also B'P perpendicular to CC and C'lJ perpendicular to B'B". If ABC is an advancing plane wave-front, the action at B' is due to that at B, and at C to that at C; and, if .'C"B" is a receding wave- front, the action at B" is due to previous action at B' and that at C" to previous action at C. Therefore the wave-front A'C"B" will be that due to the refraction of the wave-front ABC, provided the times taken for the disturV)ances to pass from B to B' to B" and from C to C' to C are the same. This will be true if PC hears the same ratio to B'Q that the velocity of the waves in the first medium (r,) does to that in the second (r-). That is, the condition is that PC _ V, B'Q ~ ■», But PC' = B'C sin (C'B'P) and B'Q = B'C sin (B'C'Q) and the angle C'B'P = oi, and the B'C'Q = a,. Hence the condition becomes angle sin «j t'. The velocity of any homogeneous train of waves-
