PRINCIPLES OF CRYSTALLOGRAPHY. 261 



§ 3.— Optical Eelations of Plane Plates whose Sides are 



Parallel. 



We shall first consider the relations of i)lane plates of crystals whose 

 sides are parallel, in straight-lined parallel light and perpendicular inci- 

 dence. Let the entering beam of parallel straight-lined light polar- 

 ized by any means, such as a nichol prism, heropathite, or a plate of 

 tourmaline, fall perpendicularly upon a plane plate of the crystal whose 

 sides are parallel. In consequence of its perpendicular incidence, for 

 we can treat parallel light always so, the beam of light enters the 

 crystal without deviation; in this defined direction only two beams, 

 whose direction of vibration is determined according to § 2 of this sec- 

 tion, can transmit themselves in the crystal, because we bring the plane 

 of the plates, which is perpendicular to the path of the beam of light, 

 into the section of the ellipsoid of polarization. 



The entering beam of light must now be divided, according to these 

 two lines at right angles to each other, into two component parts, which 

 then follow the same path entirely through the crystal; passing out of 

 it, however, they fall upon a second polarizing arrangement, the 

 analyzer, which, as the polarizer, allows the vibrating light to pass only 

 in a given direction. Here the two beams of light are divided in such 

 a way that only that component which falls in the plane of vibration of 

 the analyzer comes out of it; finally, both these components, polarized 

 in straight lines, have similar directions of vibration, and the same path, 

 and for this reason unite in a straight polarized beam of light, with the 

 same direction of vibration as component and anal3'zer. 



We suppose that both the polarizer and the analyzer are so placed 

 that their directions of vibration are parallel to 

 each other, which position is once for all deter- , ''^' ' 



mined. Let us now turn the crystal-plate in its 

 own plane until its directions of vibration come 

 together, the one, ol, (Fig. 33,) with o P of the po- 

 larizer, the other, otj, with o A of the analyzer, 

 and we have the following result : 



Straight-lined polarized light comes from the 

 polarizer in the direction of vibrating light, o P. 

 By its entrance into the crystal it will be divided ° 1 



in the direction of and or^^ which is its direction of vibration; thus no 

 component escapes, especially in the direction otj, but the beam passes 

 through the plate in the direction o f, and passes out of it with the di- 

 rection of vibration o f , falls upon the analyzer, is here divided into two 

 components, of which only the parallel one, o A, is allowed to pass 

 parallel to o A ; however, o I gives out no component, which means that 

 in this case no light whatever comes through the analyzer. 



We see also that any crystal-plate with parallel planes appears dark 

 when placed between polarizers which are at right angles to each other, 



