182 ELLIPTIC POLARIZATION. 



plane-polarized, the vibrations being in this case confined 

 to a single plane passing through the direction of the ray. 

 In intermediate eases, the polarization is called elliptical; and 

 its character may vary indefinitely between the two extremes 

 of plane polarization and circular polarization. 



(193) An elliptic vibration may be regarded as the re- 

 sultant of two rectilinear vibrations, at right angles to one 

 another, which differ in phase. 



For, let x and y denote the distances of the molecule of 

 the ether from its position of rest, in the two rectangular 

 directions ; a and b the amplitudes of the component vibra- 

 tions ; and t the time. Then 



x = a sin (vt -a), y = b sin (vt - j3) ; 

 whence 



a - j3 = arc f sin = |) - arc (sin = X \ 



Taking the cosines of both sides, and clearing the result of 

 radicals, we obtain 



This is the equation of an ellipse referred to its centre. 



When the .component rays are in the same phase, or 

 a = j3, the equation is reduced to 



which is the equation of a right line passing through the 

 origin. In this case, therefore, the vibration becomes recti- 

 linear, and the light is plane-polarized. 



When the component vibrations are equal in amplitude, 

 and differ 90 in phase y 



a = b and a-3 = 90 



