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 o 
glass at such an angle that the reflect- 
ed pencil composed of C and D has 
its planes of polarization inclined at an 
angle 9 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's ord.) 
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=3, D=3, 
E+F=1, and G+H=1. But since the planes of polarization of 
C and D are each inclined ¢ degrees to the principal section of the 
rhomb, the intensity of the light of the doubly refracted pencils will 
be as sin?g : cos*9; that is, the intensity of E will be $sin?9, and 
that of F, 4.cos?o. Hence it follows that the difference of these 
pencils, or 4 sin? — 4 cos?9, 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*@ for the whole of the polarized 
light in a pencil of eommon light C-LD. Hence, since sin?9+ 
cos?=1 and cos*p=1—sin?9, we have for the whole quantity of 
polarized light 
Q=1—2 sin?9. 
cos (1-+-7/) 
But Tan o= tan cos (i—7) * 
sin?9 
2nH— tn 2 , 
And as Tan are and sin?9-+-cos?o=1, 
we have the quotient and the sum of the quantities sin? and cos?¢» 
by which we obtain 
1 ( arta > 
it Dee a ~~  cos(i— 1’) 
x cos(t+7’)\? cos(z-+7’)\* 
(ne So 3}) sali 1+ (tan Sr) 
