EXTINCTION ANGLES. 
In this expression (<j /i) denotes the difference in phase of the two 
component periodic displacements and A the amplitude of the resultant 
vibration. 
In considering the effects which different crystals exert on transmitted 
light- waves, it has been found, both in practice and theory, that these 
influences can be predicted accurately and 
satisfactorily by reference to a triaxial ellip- 
soid, the optical ellipsoid, the position and 
relative axial lengths of which vary in general 
with different minerals and with the wave- 
length of light employed. Thus the direc- 
tions of vibration of light-waves emerging 
normally from a mineral plate are parallel 
with the major and minor axes of the ellipse 
which a central diametral plane parallel to 
the given plate cuts out of the optical ellip- 
soid for the particular mineral and wave- 
length used. The determination of the 
actual position of these directions in the plate is accomplished in polarized 
light by observing the relative intensity of the transmitted light emerging 
from the upper nicol (for different positions of the plate) parallel to the 
principal planes of the nicols. 
Light- waves after emergence from the lower nicol are plane polarized and 
their vibration is given by the equation 
FIG. 72. 
= a sin 
On entering the crystal plate this vibration is resolved into two vibrations 
in planes normal to each other. If 6 (Fig. 72) be the angle included between 
the major optic ellipsoidal axis of the plate and the plane of the incident 
vibrations, the equations for the resultant waves are 
x = u cos 6 = a cos 6 sin 
y = u sin 9 = a sin 6 sin 
2T/ 
Each of these vibrations traverses the plate with a different velocity and 
the time required by the fast wave to traverse the plate of thickness d will 
be /! = d . a', while the time required by the slow wave is ^ = d . y r where a' 
and 7' are respectively the refractive indices of the two waves. On emerg- 
ence, therefore, the equations for the periodic displacements will be 
27T 
x' = a cos d sin (t da!} 
' = a sin d sin 
On reaching the upper nicol each of these vibrations is resolved further 
into two component vibrations normal to each other, one of which, however, 
is annulled by total reflection. If <f> be the angle between the principal 
planes of the nicols, then the component vibrations emerging from the upper 
nicol are 
