Explanation of the Phenomena. — Hotchkiss. 307 
dices increases the amount of light reflected becomes 
greater. Since the contact surface of minerals in rocks is 
seldom smooth the tendency is for a large part of the light 
from A to be refracted into I>, and the condition obtains as 
shown in the figure. — that for a certain vertical distance 
along the contact, approximately equal to mn', nearly all 
the light will be on side of the mineral having the higher in- 
dex. If the objective of our microscope is focused within 
this vertical distance a band of light will be seen, if it is 
raised the band will be seen to broaden, as is evident from 
the directions of the refracted and totally reflected rays. If, 
on the other hand, the objective is lowered, the band be- 
comes narrower and finally is brighter on the side of the 
mineral of lower index. This is explained by the fact that 
the light in A, which is approximately the same in amount 
as that in B at this distance above the base of the section, 
is concentrated in a band of width mr which is shorter than 
ms and will therefore show greater intensity. As the objec- 
tive is lowered, the bright band in A and the less bright one 
in B broaden out. 
If rays from B are incident upon y-z at an angle less 
than the critical angle (62 10' in the case illustrated), they 
will not be totally reflected but will partly pass through 
into A. If there is sufficient light thus refracted a bright 
band will be seen in A as well as in B when the objective is 
raised. It is important therefore to diaphragm the light 
entering the condensing system to such an extent that all 
the light from 15 is totally reflected at the contact surface. 
This increases the relative brightness of the band seen in B. 
Computations of the different values of the distances 
from y to m and n were made for other indices besides the 
two figured. The angles of incidence of the four converg- 
ing rays were taken as 45 and 20 as in the figure and the 
distance from x to y was taken as unity. 
It is evident from this table that the distance from n to 
n' (see fig. 1) is quite within the range of observable quan- 
tities even for slight differences in index of refraction. The 
lengths of yn and ym for indices of 1 . 54 and 1 . 56 were com- 
