292 FRESNEL ON DOUBLE REFRACTION. 



of each system of waves in the crystal from the direction of its 

 plane relatively to the axes. 



Demonstration of the Law of Refraction for plane and indefinite 



Waves. 

 Let, for example, I N (fig. 7) be the plane of the incident wave, 

 which I suppose for greater simplicity parallel to the face by which 

 ■p,. ^ it enters the prism of crystal BAG, whose 



axes moreover have any directions what- 

 ever ; all the portions of this wave will ar- 

 rive simultaneously at the plane A B, and 

 it will not undergo any deviation of its plane 

 in penetrating and traversing the crystal. 

 This will no longer he the case when it 

 y^^ 'h=-'---- / emerges from the prism : to determine the 



E "" - direction of the plane of the emergentwave, 

 from the point A as centre and with radius A E equal to the 

 path described by the light in the air in the time during which 

 the wave advances from B to C, describe the arc of a circle, to 

 which through C draw the tangent C E ; this tangent will indi- 

 cate precisely the plane of the emergent wave, as is easily proved*. 

 If we consider each disturbed point of the surface A C as be- 

 coming itself a centre of disturbance, we see that all the small 

 spherical waves thus produced will arrive simultaneously at C E, 

 which will be their common tangent plane : now, I say that this 

 plane will be the direction of the total wave resulting from the 

 union of all these small elementary waves, at least at a distance 

 from the surface of considerable magnitude relative to the length 

 of an undulation ; in fact, let H be any point of this plane for 

 which I seek to determine in position and in intensity the re- 

 sultant of all these systems of elementary waves. The first ray 

 arrived at this point is that which has followed the direction 

 G H perpendicular to C E ; and the rays g H and g^ H, starting 

 from other points g and g' situated on the right and left of G, 

 will be found behindhand in their route by a whole or fractional 

 number of undulations, so much the greater as these points are 

 further oflffrom the point G. If now C A be divided in such a 

 manner that there maj'^ be always a difference of a semi-undula- 

 tion between the rays emanating from two consecutive points of 



• I suppose the plane of the figure perpendicular to tlie two faces of the 

 prism. 



