54 
SIR DAVID BREWSTER ON THE PHENOMENA OF THIN PLATES 
Inclination of the planes of polarization of the two pencils, (j> and <p"'. 
Angles of 
Incidence. 
Azimuth 22° 30'. 
Azimuth 45°. 
Azimuth 67° 30'. 
Azimuth 80°. 
Pencil from 
first surface. 
Pencil from 
second surface. 
Pencil from 
first surface. 
Pencil from 
second surface. 
Pencil from 1 Pencil from 
first surface, second surface. 
Pencil from 
first surface. 
Pencil from 
second surface. 
0 
10 
20 
30 
40 
50 
56in45 
60 
70 
80 
85 
90 
22 30 
21 42 
19 11 
15 25 
10 18 
4 18 
0 0 
2 6 
7 54 
15 11 
18 40 
22 30 
22 30 
22 5 
19 34 
15 55 
11 1 
4 52 
0 0 
2 35 
11 52 
24 41 
33 34 
43 57 
45 0 
43 51 
40 13 
33 40 
23 41 
10 18 
0 0 
5 4 
18 32 
33 13 
39 12 
45 0 
o / 
45 0 
44 24 
40 38 
34 33 
25 11 
11 37 
0 0 
6 13 
26 53 
47 58 
58 2 
66 44 
67 30 
66 40 
64 13 
58. 7 
43 21 
23 41 
0 0 
12 5 
39 0 
57 41 
63 5 
67 30 
67 30 
67 4 
64 14 
58 58 
48 37 
26 24 
0 0 
14 44 
50 45 
69 32 
75 30 
79 54 
O / 
80 0 
79 36 
78 13 
75 10 
68 6 
45 52 
0 0 
26 42 
62 16 
74 56 
77 48 
80 0 
o / 
80 0 
79 48 
78 23 
75 38 
68 6 
49 23 
0 0 
31 42 
70 49 
80 58 
83 43 
85 40 
The results in this Table, which may be considered as those of observation*, exhibit 
at one glance the general phenomena at all angles of incidence and azimuth. 
The two interfering pencils are in every case reflected at angles either both above 
or both below the polarizing angle, and hence their planes of polarization are always 
on the same side of the plane of reflexion and in the same quadrant, and consequently 
they never can be at right angles to each other so as to prevent interference. For 
the same reason the inclination of the planes never can exceed 90°, so as to produce 
the complementary white-centred rings, in conformity with the law previously given. 
If, for example, we compute the value of x in the preceding formula at an inci- 
dence of 70°, we shall find it 66° 25', at which azimuth the inclinations <p and <p"' of 
the planes of polarization are 40° 47', and 49° 53' ; but though the sum of these an- 
gles is 90°, yet the real inclination of the planes is <p'" — ® = 9° 6'. 
This property of parallel transparent films, of giving by reflexion pencils polarized 
in planes at various inclinations, when the incident light is polarized in different 
azimuths, enables us to obtain two pencils of polarized light, inclined at any angle, 
varying from 0° to 21° 44' in glass, and to study the phenomena which such pencils 
exhibit, either in their mutual action, or in their relations to other properties of light. 
But the phenomena become more varied and interesting when the second surface 
of the plate is inclined to the first. In this way we may produce effects analogous to 
those produced by a change in the refractive power of the second surface by contact 
with another refracting surface, and obtain pencils inclined 90° to each other, and 
therefore exhibiting the white-centred rings. The phenomena will in this case re- 
semble those of a film of oil upon water. 
When the refractive index of a parallel film exceeds T508, the ray is incident on 
the second surface at an angle less than the polarizing angle ; but by inclining the 
* See Philosophical Transactions, 1830, pp. 74, 138. 
