OPTICS. 137 
line is drawn through the middle of the anterior half of the inner ring, 
which has its edges somewhat bevelled; a vertical plane passed through 
this line and the centre of the ring, would be parallel to the plane of 
reflection from the upper mirror. When the index stands at 0° or 180°, the 
planes of reflection of the two mirrors coincide ; they are perpendicular to 
each other when the index points to 90° or 270°. If the upper mirror, like 
the lower, be adjusted at an angle of 35° 25’ with the vertical line, the 
index standing at 0° or 180°, then a ray from the lower mirror will be 
reflected, and the field will appear bright; if, on the contrary, the index 
stand at 90° or 270°, this same field will be dark. Thus, from 0° to 90° the 
brightness decreases ; from 90° to 180° it increases; from 180° to 270° it 
decreases again; and from 270° to 180° it again increases. There is 
generally a second ring interposed between the two mirrors, upon which a 
glass plate may be laid, to hold objects which are to be examined by 
polarized light. 
The preceding angle of 35° 25’ is that in which the light reflected from 
glass is completely polarized ; this is then called the angle of polarization. 
At any other angle the polarization will be only partial or incomplete. 
Every substance has its angle of complete polarization, this being obtained, 
according to Brewster, by the following formula: the index of refraction is 
the tangent of the angle of polarization. In pl. 21, fig. 70, if si be the 
incident and fi the reflected ray, fir a right angle, then if’ will be the 
angle of polarization. A plane passed through abc (fig. 69) is called the 
plane of polarization. When a ray is polarized by reflection, as in the 
illustrations already adduced, its plane of incidence is at the same time its 
plane of polarization. 
Rays of light may also be polarized by refraction. Thus, if a ray be 
incident on a transparent glass plate, at the angle of polarization, it will be 
partly reflected and partly refracted. The reflected portion will be 
polarized, and the refracted also, but in a less degree. By employing a 
bundle, consisting of several glass plates, the polarization of the refraction 
will be increased in intensity. An arrangement of this latter character 
may be substituted for the analysing plate in the apparatus represented in 
jig. 59, by removing the upper ring with its plate, and replacing it by a 
ring carrying a hollow cylinder. In this cylinder is to be placed the tube 
( fig. 101), with its bundle of glass plates, as represented in the figure. 
The analysing plate of the polariscope (fig. 69) may also be replaced by 
a plate cut from a crystal of tourmaline, the surfaces being taken parallel to 
the principal axis. Even common light will be polarized by passing through 
such a plate. Two plates of this character applied to each other, with their 
axes parallel, transmit light like a single plate of the same thickness. By 
rotating one of them on the other, the same variations in the intensity of 
light as in the polariscope will be presented: a diminution from 0° to 90°, 
and from 180° to 270°: an increase from 90° to 180°, and from 270° 
to 360°. 
In the phenomena of double refraction we have another illustration of 
polarization. Certain transparent bodies possess the property of splitting 
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