METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
(3) 
Let 7*1=1.700 
Thenfora 2 = 3 
2=I-7 O1 tt* 2 Wl = O.OO34 
Si = o (limiting angle) 
2 34' 
From these examples, as well as from the formulas, it is evident that the 
greater the difference between the refractive indices n\ and 2, the larger 
the limiting angle for complete total reflection and therefore the greater the 
difference in light intensity between both sides. Thus, if a cone of rays of 
angle a = 30 be used and n\ = i . 55, the refractive index n z must equal i . 629 
or more for complete total reflection. It is significant that for differences of 
only o.ooi between n\ and w 2 the limiting angle necessary to produce com- 
plete total reflection is over 3 degrees. By lowering the condenser and 
stopping down the diafram this angle is easy to obtain and with it the most 
favorable conditions for the observation of the Becke line. The greater the 
difference in refractive indices between two adjacent plates, the wider the 
FIG. 58. 
cone of rays permissible to show differences in refraction clearly. By clos- 
ing the iris diafram or by lowering the condenser and observing the phe- 
nomena thereby produced, it is possible, therefore, to estimate approxi- 
mately the relative difference in refringence between two adjacent mineral 
plates or between Canada balsam and a mineral plate embedded in it. 
In case the junction plane between the two mineral plates is not vertical, 
but inclined, the deflection of the rays is illustrated for the different possible 
cases in Fig. 58. These are drawn angle true for the refractive indices 
i = i . 55, j = i . 60 and for an angle of inclination of 40 of the junction line 
with the normal to the section. In all cases it is evident that the rays are 
deflected toward the higher refracting substance. But in the case where n\ 
is above w 2 (Fig. 58, b\, c^} and a cone of rays is used, as in the Becke line 
method, either total reflection of the rays may take place and they be de- 
flected toward Wi or part or all of the rays may be refracted in n\, as in Fig. 
