ON THE REFLEXION AND REFRACTION OF LIGHT. 265 



where to abridge, the characteristics only of the functions are 

 written. 



By means of the last four equations, we shall readily get the 

 values of F "%"//"%/" in terms of/", and thus obtain the inten- 

 sities of the two reflected and two refracted waves, when the 

 coefficients A and B do not differ greatly in magnitude, and the 

 angle which the incident wave makes with the plane surface of 



junction is contained within certain limits. But in th,e intro- 



j^ 

 ductory remarks, it was shewn that -g = a very great quantity, 



which may be regarded as infinite, and therefore g and g t may 

 be regarded as infinite compared with 7 and 7,. Hence, for all 

 angles of incidence except such as are infinitely small, the waves 

 dependent on tf> and <f> t cease to be transmitted in the regular 

 way. We shall therefore, as before, restrain the generality of 

 our functions by supposing the law of the motion to be similar 

 to that of a cycloidal pendulum, and as two of the waves cease 

 to be transmitted in the regular way, we must suppose in the 

 upper medium 



^ = a sin (ax + by + ct + e)+j3 sin ( ax + ly + ct + <?,) 

 and = e a '* (A sin f + B cos f ) 



and in the lower one 



^snCa/c + fy + c*) I 



, = e-> (A t sin ^r fl + B t cos ^ J 



where to abridge ^ = ly + ct. 



These substituted in the general equations (14) and (15), 

 give 



= 9? (- / 2 + & 2 ), 

 or, since g and g t are both infinite, 



b = a'=o/. 



It only remains to substitute the values (20), (21) in the 

 equations (17), which belong to the surface of junction, and 

 thus we get 



