460 HISTORY OF SCIENCE. 



centre of disturbance ; therefore draw from c as a centre, with radius = 

 G D, the semicircle K H ; and from G draw the tangent G H. The line 

 G H is the position of the wave-front after reflection. Join c H and 

 produce towards L, and from G draw G M at right angles to H G. c L 

 and G M are the direction of the reflected ray, and very little geometry 

 is required to prove that this result agrees with the experimental law 

 of reflection t.e., the angles of incidence and reflection are equal. 

 To show that this construction applies to every point in the wave-front, 

 take any point in c D as N, draw N o parallel to F G, and o P parallel to 

 N D. Then a circle drawn from o with radius = G P will just touch 

 the line H G, and the reasoning which applies to points D and c will 

 equally apply to P and o. Imagine that the same construction is made 

 for every point in c D as for N, then will the semicircles all have H G 

 for their common tangent ; that is, the waves they represent will all 

 concur by arriving at G H in one and the same phase, and G H is the 

 only locus in which all the reflected waves will so concur.* The front 

 of the reflected wave can therefore be no other than G H. We have 

 here spoken of drawing semicircles, but properly speaking it is by hemi- 

 spherical surf aces that the reflected wave-fronts would be defined. The 

 semicircles in the diagram may be considered as sections of the hemi- 

 spheres by a plane containing their centres, and there will be little 

 difficulty in conceiving that in this series spherical surfaces can concur 

 only in the plane H c G to produce a wave-front. 



For the case in which undulations are supposed to pass from one 

 medium to another, Huyghens' principle requires a construction similar 

 to that given for refraction on page 227, to which the reader is requested 

 to refer. Let us suppose that the shaded portion of Fig. 1 1 1 represents 

 water, and that the space above c D is air. In the case supposed, the 

 wave-surfaces are spherical ; but in the majority of cases where light 

 is refracted by a solid body, the velocity of propagation is not uniform 

 in all directions within the body, and the form of the wave-front is deter- 

 mined accordingly. Such, at least, is the theory by which Huyghens 

 was able to explain the phenomena of refraction presented by Iceland 

 spar phenomena since found, in fact, to obtain to some degree in 

 all except one class of crystals. It will be readily seen on inspection, 

 that, in Fig. T 1 1, the angle B A B'is equal to the angle of incidence (/"), 

 since each of these is the complement of angle B B' A. Similarly the 

 angle of refraction, or (r), = angle A B'/ Now (page 61) ||, = sine /", 

 and %, = sine r; therefore, $51! = f? : but B B' : A/ = velocity of 



AB' ' sine r A/ } J } 



light in air : velocity of light in water. It follows, therefore, that the 

 index of refraction (page 156) between two media is the ratio of the 

 velocities of light in these media. For instance, the index of refraction 



* If the reader has any difficulty in realizing this mentally, he is recommended to take 

 a ruler and compasses, and actually draw on a piece of paper for a considerable number 

 of points the construction indicated in the text. 



