M:AG = v':v, (6.2) 



and (2) at each point K describe an arc with radius v '/v times 

 the corresponding length KM. Therefore, the line NB is obtained 

 as the new wave front after refraction and this is the envelope 

 of the spherical wavelets originating at K,K,K. 



The angles of incidence and refraction are seen from figure 3 

 to be CAB and NBA, respectively, and they are located in the two 

 right-angled triangles whose common hypotenuse is AB, Thus, by 

 taking the sines of the angles, we have by construction 



sin CAB _ CB/aB ^ v_ //- ^.n 



sin NBA " NA/AB v' ^ '^^ 



or 



42^ = ^ = R (6.4) 



sin r v' 



where 1 and r denote the angles of incidence and refraction, 

 respectively. 



Barton concludes, "This consequence of Huygens ' principle 

 that the ratio of the sines is constant, is seen to be in accord 

 with the well-known optical laws of refraction. The same laws 

 are valid for acoustics also." 



To illustrate Snell's law for ocean waves, we have constructed 

 a rectangular plastic "step" model which when submerged in the 

 ripple tank is one and one half inches from the bottom, in water 

 one and three quarters inches deep. We may now say that for certain 

 wave lengths part of the tank contains shallow water and part of 

 the tank contains deep water, the zone of transition being a straight 

 line, in two dimensions. 



14 



