6l6 ADAMS AND WILLIAMSON: BIREFRINGENCE AND STRESS 



tended along OX and OZ. The velocity of the beam of light 

 will be altered and in general the wave will be split into two wave 

 fronts proceeding with different velocities and polarized in direc- 

 tions at right angles^ to each other. Moreover, a ray of polar- 

 ized light after passing through the block of glass in a direction 

 normal to the surface will remain a single ray but will be found 

 to be elliptically polarized and may best be treated as the re- 

 ^iltant of two rays vibrating, respectively, along OY and OZ 

 and differing in phase^ by a certain amount. The compressed 

 block of glass thus behaves as a uniaxial crystal whose optic 

 axis is parallel to OF. 



Now a thrust in the direction OZ will produce an effect 

 similar to that in the direction OY, for the cube will be com- 

 pressed in the direction OZ and extended along OY , but a thrust 

 parallel to OX will produce no phase difference of the rays 

 vibrating along OY and OZ since the cube is extended the same 

 amount in these two directions. 



It is evident, therefore, that when a beam of light passes 

 through a block of strained glass the velocity of the Ught (and 

 hence the refractive index of the glass) depends on (i) the direc- 

 tion of vibration of the light, and (2) the dilatations in those 

 directions perpendicular to the path of the beam of light. 



THE GENERALIZED EQUATIONS 



The equations used by Neumann ^° for expressing the influence 

 of elastic deformation on the propagation of light are as follows : 



•Vx = V -[- qXx + pyy + pZz (Ia) 



Vy = V -{- px^ -f qyy + pz.^ (Ib) 



Vz = V + pXjc + pyy + qzz (ic) 



* A ray of light by reflection from a polished surface becomes partially or completely 

 polarized. The plane of polarization is arbitrarily defined as the plane containing 

 the incident and reflected rays, and the direction of vibration is usually taken as 

 the normal to the plane of polarization. The vibration direction so defined is the 

 direction of the electric vibrations of the electromagnetic disturbances and is per- 

 pendicular to the magnetic vibrations. 



^ In the actual measurement of birefringence the beam of polarized light is usually 

 arranged to vibrate in a direction at 45° from OF or OZ. The phase difference 

 obviously may be expressed as a path difference by taking account of the wave 

 length of the light. 



1' F. NEtnviANN. Ann. Phys. 54: 1841. 



