Plane waves are generated in deep water and travel into 

 shallow water crossing the zone of transition at a particular 

 angle of incidence (fig. 4), Upon entering shallow water at 

 normal incidence, the wave crests are not deflected, but it is 

 observed that the wave length has decreased appreciably. The 

 expression for the velocity of a plane wave in water of any depth 

 is 



V = ^ (6.5) 



where T is the period and L is the wave length. From (6,5)? the 

 velocity varies directly as the wave length. Therefore, as the 

 wave length decreases upon entering shallow water, the velocity 

 decreases proportionally, the period remaining constant. 



Measurement of the angles of incidence and refraction, and 

 of the wave velocities in the deep and shallow water (by means of 

 the wave length), will verify Snell's law, when these data are sub- 

 stituted in (6.4). 



Another proof of Snell's law and a discussion of the behavior 

 of the refracted and reflected waves has been given by Coulson 

 (1943). 



Suppose that the ratio of the sine of the angle of incidence 

 to the sine of the angle of refraction is less than one. Then the 

 angle of refraction is greater than the angle of incidence. However, 

 the limiting value of sin i and sin r is one, therefore when i = 90°, 

 sin i = 1, and sin r must be greater than 1, to maintain the con- 

 dition that sin i/sin r<l. This, of course, is impossible. Since 

 it is necessary that the ratio of the sines be constant in (6.4), 

 failure to satisfy the condition above usually occurs at some angle 



15 



