It is found that the disturbance in the second medium has 

 the form 



_2v_ /siiife _ , 

 TV / ? 



It is seen from (11.2) that the superficial wave has an 

 amplitude ^r'A at the surface along the x-axis, which decreases 

 exponentially with z. Furthermore, the energy of the superficial 

 wave is propagated parallel to the surface along the x-axis, thus 

 the energy-flux across any element of area of the surface must 

 be zero. Since there is no energy-flux across the boundary, it 

 follows that the amplitudes of the incident and reflected waves 

 must be equal. Hence, we have total reflection. 



If a rigid plane is placed at the boundary between the two 

 media then the phenomenon which occurs is the same as demonstrated 

 in figxire l6. 



That this is the case can be seen by placing a plane strip 

 of plastic at the boundary of the step model in an earlier experi- 

 ment. If the strip of plastic extends above the water, then we 

 have the case of total reflection by a rigid plane (figure 17) • 

 Comparison of figure 17 with figure 16 bears out the theory 

 already discussed, although in figure l6, there is some leakage 

 of energy across the boundary, due to a poor deep water to shallow 

 water ratio. 



The laws of reflection which are valid for light waves and 

 sound waves have now been shown by theory and experimentation 

 (sections 9j 10, and 11), to hold also for water waves, and so 



38 



