DOUBLE IIEFRACTION OF CRYSTALS. Ill 



Let US suppose the surfaces of entrance and emission, which Case of paral- 

 we will call the first and second faces, to be parallel to each ^^' suifaces. 

 other. Let the thickness of the crystal be imperceptible, yet 

 greater than the sum of the radii of the spheres of activity of 

 the two faces. In this case it will be demonstrated, by the 

 preceding reasoning, that the four reflected pencils will form 

 but one perceptibly, being in the plane of incidence of the ge- 

 nerating ray, and forming with the tirst face an angle of reflec- 

 tion equal to the angle of incidence. Now let us restore the 

 crystal to its proper thickness : it is clear, that, in this case, the 

 reflected pencils, after issuing from the first face, v ill assume 

 directions parallel to those they had taken in the former case : 

 these pencils, therefore, will be parallel to each other, and to 

 the plane of incidence of the generating ray; only, instead of 

 being confounded to the senses, as in the former case, they will 

 be separated by distances so much the greater, as the crystal is 

 thicker. 



Now, if we consider any given interior r3y issuing out in 

 part by the second face, and in part reflected by it into two pen- 

 cils, the issuing ray will be parallel to the generating ray ; for 

 the light, as it issues out of the crystal, must take a direction 

 parallel to that it had on entering into it ; since, the faces of 

 entrance and exit being supposed parallel, it is acted on at its 

 exit by the same forces as it was at its entrance, but in the op- 

 posite direction. In the direction of the issuing ray, let us 

 conceive a plane perpendicular to- the second face ; and in this 

 plane let us imagine a right line, exterior to the crystal, passing 

 through the point of exit, and forming with the perpendicular 

 to the face, but on the side opposite to the direction of the is- 

 suing ray, the same angle as that direction ; lastly, let us con- 

 ceive a ray of light entering the crystal according to this right 

 line. This ray, at its entrance, will be divided into two others, 

 which, at issuing out of the crystal by the first face, will take 

 directions parallel to that of the ray before its entrance by the 

 second face ; they will be visibly parallel to the directions of the 

 two reflected pencils ; which cannot take place but as far as the 

 two rays, into which the ray of light is divided on entering by 

 the second face, confound themselves respectively in the interior 

 of the crystal with the directions of the two reflected pencils. 

 But the law of Huygens gives the directions of the rays into The law of 



which 



