OPTICAL PROPERTH 8 01 CRYSTALS 



171 



ray i- t ailment to the sphere or wave front of the ordinary ray at two 

 points p Mini p', where the crystallographical axis c cuts them. The 

 sphere in this case, that of calcite, an optically negative crystal, 

 i- entirely inclosed by the oblate ellipsoid. In the case of quartz, 

 an optically positive rry-tal, the wave front of the extraordinary 

 ray is represented by a prolate ellipsoid of revolution, which is in- 

 do>ed within the circle or sphere, as represented in Fig. 315. 



Optically biaxial crystals. - The wave front in crystals of the 

 orthorhombic, monoclinic, and triclinic systems is not an ellipsoid 

 of revolution, but a combination of two wave surfaces, one within 

 the other, continuous at four depressions, Fig. 316, or symmetrical 

 points, the position of which depends upon the relative values of 

 the three indices of refraction. This fourth dimensional surface is, 

 however, symmetrical to three planes of symmetry intersecting 

 each other at right angles, in three straight lines, analogous to the 

 axes and planes of the orthorhombic system. The three lines of 

 intersection always represent directions within the crystal parallel 

 to which there is a maximum or minimum velocity of light, as all 

 such crystals have three indices of refraction. They are repre- 



GL ~l~ 6 | V 



sented by a, p, and \. The mean index of refraction is - J > 



<J 



and -y a will always represent the greatest double refraction, as 

 ^ is the greatest and a the smallest index. 



FIG. 316. 



FIG. 317. 



Sections of the wave front in the three planes of symmetry are 

 represented in Figs. 316, 317, 318. It will be noted that in each case 

 there is a circle and an ellipse, or for each of these sections there are 



