OF ELLIPTIC POLARIZATION. 
325 
This conclusion is not opposed by any of the phenomena, when we consider 
merely the mean refrangible ray to which these numbers refer : but when we 
use homogeneous light, a very strange anomaly occurs. The maximum angle 
of elliptic polarization for red light in the case of silver is 75° 30', and for blue 
light /0° 30', giving 
Angle. 
Index of refraction for red light 
. . . . 3.866 . 
. . 7°5 30 
mean ray 
. . . 3.271 . 
. . 73 0 
blue light 
. . . . 2.824 . 
. . 70 30 
the order of the refrangibilities being inverted. 
The perfect similarity between the action of metals, and the total reflexion 
of the second surfaces of transparent bodies, promised to throw light upon this 
difficulty. I accordingly examined the formula of Fresnel for total reflexion, 
where the phase P is thus expressed : 
~ „ 2 m? (sin if — ( m 3 + 1 ) (sin if + 1 
Cos P = — — l . — - v / , ■ ■ . 
From this formula it follows that when m = 1.51, and i — 54° 37', P will 
be 45° for one reflexion, and consequently for two reflexions 2 P = 90°. If m 
increases as it does for blue light, then the phase will be 45° at an angle of inci- 
dence above 54° 37', that is, the circular polarization of the pencil will take 
place at a greater angle of incidence for blue than for red light, which is the 
reverse of what takes place in metals. Upon making the experiment, however, 
with total reflexion, we shall find that the blue rays are circularly polarized by 
two reflexions at a less angle than the red rays, thus approximating the two 
classes of phenomena even with respect to this singular anomaly. Hence in 
order to accommodate M. Fresnel’s formula to homogeneous light of different 
colours, let m be the index of refraction for the homogeneous ray, and d the 
difference between it and the mean index, then the formula for the phase P 
„ 2 (m + <7) 2 (sin if — (( m + df + l) (sin if + 1 
will become Cos P = — — ,) r , ■ 
((m ± df + 1 J (sin *)* + 1 
they reflect is a function not only of their refractive power, but of their transparency, which will be 
proportional to the intensity of the reflected pencil that has entered the metal. If this is the case, 
the transparency will be proportional to the inclination of the plane of the restored ray after two re- 
flexions at the maximum polarizing angle, and the order of the transparencies of the different metals 
will be that of the Table, p. 294. See Mr. Herschel’s Treatise on Light, § 594, 845. 
