i 
284 On Polarization of Light by Reflexion. 
which are produced by a single reflexion, and we may therefore 
apply it in our future investigations. 
Let us now suppose that a beam of common light, composed of 
two portions A, B, (Fig. 2,) polarized +45° and —45° to the plane 
of reflexion, is incident on a plate of 
glass at such an angle that the reflect-_ 
ed pencil composed of C and D has 
its planes of polarization inclined at an 
angle @ to the plane MN. When a 
rhomb of calcareous spar has its prin- 
cipal section in the plane MN, it will 
divide the image C into an extraordi- 
nary pencil E and an ordinary one F'; 
and the same will take place with D, 
G being its extraordinary and H its ordinary image. If we represent 
the whole of the reflected pencil or C+D by 1, then C=$, D=3, 
E+F=1, andG+H=1. But since the planes of polarization of 
C and D are each inclined 9 degrees to the principal section of the 
rhomb, the intensity of the light of the doubly refracted pencils will 
be as sin?9 : cos’; that is, the intensity of E will be 3 sin?9, and 
that of F, 4.cos?~. Hence it follows that the difference of these 
pencils, or 4 sin? — $ cos?@, will express the quantity of light which 
has passed from the extraordinary image E into the ordinary one F’, 
that is, the quantity of light apparently polarized in the plane of re- 
flexion MN. But as the same is true of the pencil D, we have 
2(4 sin?9¢—4 cos*@) or sin?9—cos?q for the whole of the polarized 
light in a pencil of common light C+D. Hence, since sin?9+ 
cos?9=1 and cos?7=1—sin?9, we have for the whole quantity of 
polarized light 
Q=1—2 sin’. 
cos (t-+7’) 
But Tan p= tan ve 7 
sin?0 : 
2 ya 2 ee 
And as Tan? costa and sin?g-++cos?9=1, 
we have the quotient and the sum of the quantities sin?9 and cos?¢@, 
by which we obtain 
1 i « Ay? 2 
tt atlas 
Sin?o= i cos(t—# ), 
een ( cos(t+2’)\ ? 
(ta ” cos(i—?’) ne ie tane ow} 
