to the Wave Theory of Light. 45 



If the surface of refraction should happen to have a node 

 N) which is a point of intersection where it admits an infinite 

 number of tangent planes (3), let the direction of the incident 

 ray S'OS be chosen, so that the right line US perpendicular 

 to the face of the crystal, being produced below 8, may pass 

 through N, and we shall have a cone of refracted rays formed 

 by the perpendiculars let fall from upon the tangent planes 

 at -ZV; all of which rays, on emerging parallel to OS from the 

 second surface of the crystal, will be in complete accordance 

 with one another. For we have just seen that if the ray S'OS 

 were supposed to emerge after being refracted in the ordinary 



ON 



way with an index equal to -^-~, it would be in complete 



accordance with any ray of the cone. 



48. The interval between any two rays emerging at the 

 same side of the crystal is the difference of their retardations. 

 In taking the difference, the letters that are common to the 

 names of the two rays may be left out. Thus the ray SPmMS 

 is behind the ray SPS by the interval 



The line -7-^ Pp is the interval between the rays SMS and 

 OS 



SMpPS, or between the reflected ray Os and the ray SPps, 

 and so on. 



49. The retardations of the two refracted rays SPS and 



Q 

 SMS, emerging without internal reflection, are -^ SP and 



PM 



-y~- SM respectively. The difference of these is 9 -y~ . Con- 



sequently, when the two refracted rays have emerged from the 

 second surface in directions parallel to the incident ray, the 

 light in the plus emergent ray is behind the light in the minus 



emergent ray by an interval equal to ^o Or, in other 



(Jij 



words, the incident plane wave, perpendicular to OS, produces 



