OPTICAL PROPERTIES OF CRYSTALS 



173 



velocity, arc all rout allied in the one plane ; this plane is known as the 

 plane of the optic axes or axial plane, abbreviated to (Ax. PI.). The 

 line bisect inn the ^nailer angle between the optic axes is the acute 

 bisectrix (Bx a ) or first median line ; the line bisecting the larger 

 aniile is t he obtuse bisectrix (Bx ). The internal angle between the 

 acute bisectrix and the optic axis is represented by V and 2 V = pop', 

 t he angle between the optic axes, always less than 90 and measured 

 within the crystal. When measured in air the angle is designated 

 2 E ; 2 E owing to refraction is always larger than 2 V and is often 

 180 from total reflection. The value of 2 V varies with different 

 substances and will depend upon the indices of refraction. When 

 the three indices are known, the angle 2 V may be calculated from 

 the formula : 



tan V = 



As the indices of refraction vary with the wave length or color of 

 light, it will be seen that 2 V for violet light will differ from the value 

 of 2 V for red light ; their dif- 

 ference will measure the disper- 

 sion of the optic axes. 



The optical sign of biaxial 

 crystals. The intermediate in- 

 dex of refraction f3 in different 

 biaxial crystals may vary from 

 a as a minimum to ^f as a maxi- 

 mum limit. 



In Fig. 319, as the value of p 

 decreases the circle ycy' will ap- 

 proach the circle yxy' and the 

 radius oc will approach ox. (The 

 figure is drawn with the three 

 axes ox, oy, and oz proportional 

 to the indices of refraction.) 

 The four points marked c will 

 draw nearer to x, while the optic axes, perpendicular to these circular 

 cross sections, will also draw nearer each other, constantly decreasing 

 the angle 2 V, pop' ; when P = a, c reaches x and p, p' reaches Z ; 

 in which case the angle between the optic axes is zero and the cross 



FIG. 319. 



