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XI. On the Refraction of Plane Polarized Light at the Surface of a Uniaxal Crystal. 
By R. T. Glazebrook, M.A., Fellow and Assistant Lecturer of Trinity College, 
Demonstrator in the Cavendish Laboratory, Cambridge. 
Communicated by Lord Rayleigh, M.A., F.R.S. 
Received October 27,—Read November 17, 1881. 
The laws of the reflexion and refraction of polarized light at the surface of a crystal 
in accordance with the electro-magnetic theory of light have been discussed by 
Lorentz (Schlomilch Zeitschrift, vol. xxii.), Fitzgerald (Phil. Trans., Vol. 171, 1880), 
and myself (Proc. Camb. Phil. Society, 1881). When a plane wave of electro-magnetic 
disturbance falls on the surface of separation between two different dielectric media 
six equations of condition are obtained. Three of these express the conditions that 
the electric displacement perpendicular to the surface and the electromotive force along 
the surface should be the same in the two media, while the other three do the same for 
the magnetic force and displacement. In all cases the six equations reduce to only 
four. 
Let us suppose we know the amount and direction of the electric displacement in the 
incident wave. If both media are isotropic, these four equations give us the amounts 
and directions of the electric displacements in the reflected and refracted waves. 
If the second medium is crystalline the possible directions of vibration in a wave 
travelling in it are known when the position of the wave is known ; two of the 
equations as before give the amount and direction of the electric displacement in the 
reflected wave, the other two give the amounts of the displacements in the two 
refracted waves; the directions of these displacements being known from the position 
of the waves with reference to the axes of the crystal. 
In general we have two refracted waves, the ordinary and extraordinary. Now, 
according to the electro-magnetic theory, light obeys the same laws as to propagation, 
reflexion, and refraction as this electro-magnetic disturbance, and the direction of the 
light vibrations coincides with that of the electric displacement, while the intensity of 
the light is measured by the energy of the disturbance. Our equations then give us 
the intensities of the two refracted rays which arise in general when a wave of 
polarized light falls on a crystal. 
Consider now such an incident wave. Experiment tells us that there are two 
positions for its plane of polarization, in either of which one or other of the refracted 
waves disappears. I he same result follows from the theory, and if we know the 
