130 POLAEIZATION BY REFRACTION. 



mirror is rotated ia azirautli, its plane of incidence and reflection is constantly 

 changing its inclination to the plane of polarization of the ray incident npon it. 

 Suppose tlic incidence upon the second mirror not to be at the polarizing angle. 

 It is found that after reflection in an oblique azimuth, the plane of polarization 

 is nearer to the plane of reflection than it was at incidence. If the azimuth at 

 incidence be represented by a, and that after reflection by «', there will be found 

 to be a constant ratio between tana and tana'; tana' being always less than 

 tana. By many reflections, with the same azimuth between the mirrors, 

 the plane of polarization may be brought indefinitely near to the plane of re- 

 flection; but it can never be made, in this way, absolutely coincident with it. 



When common light is reflected from any surface at an angle greater or less 

 than the polarizing angle it is found to be partially polarized : that is to say, it 

 is made up of a mixture of polarized light Avitli common light. By repeated 

 reflections at the same incidence the polarization may be made sensibly com- 

 plete. ■ The number of reflections necessary for this purpose Avill be greater as 

 the angle of incidence is further from the polarizing angle. 



It must not be overlooked that, though at the angle Avhich we have called 

 the polarizing angle, all the light that is reflected is polarized, yet that this is 

 after all but a small portion of the incident light. From a single surface of 

 glass it amounts to less than eight per cent. The manner of determining this 

 ratio will be seen hereafter. When, for purposes of experiment, it is desired to 

 obtain a large and intense beam of polarized light, it has accordingly been found 

 useful to employ many reflecting plates placed one upon another, forming a 

 hundle or pile. It is obvious that the thinner these plates are made, (so that 

 they are not so thin as to produce color,) the more convenient they will be in 

 use, and, from the diminution of absorption, the more economical of light. Not 

 fewer than sixteen are usually employed. 



The amount of light reflected at difterent angles of incidence goes on increas- 

 ing from 0° to 90°. The amount which is pola: -^ed in the reflected beam also 

 goes on increasing, but not throughout the quadrant. For glass having the 

 index 1.5, the incidence of maximum polarization is 79°. At this incidence 

 the total intensity of the reflected light is expressed by the decimal 0.355, the 

 intensity of the incident light being 1. The amount which is polarized in the 

 reflected beam is, however, only 0.1518, which is still about double of that which 

 is reflected at the polarizing angle. But, comparing this value with the fore- 

 going 0.355, we shall see that it is less- than half th(> total light reflected, (forty- 

 four per cent.,) and accordingly it is not suited to exact experiments in polariza- 

 tion. 



When a transparent reflector is employed as a polarizer the transmitted beam 

 will be found to contain light which is polarized in a plane perpendicular to the 

 plane of refraction. The amount of light so polarized is exactly equal to the 

 amount polarized at the same time by reflection, and in the plane of reflection. 

 And as the maximum amount polarized by reflection from one surface of glass 

 having the index 1.5, is 0.1518, this also is the maximum amount which can be 

 polarized at one surface by refraction. But since, at this angle of maximum 

 polarization, the total reflection is only 0.355, the total transmission will be 0.645, 

 and of this amount the polarized portion will be but twenty-three and a half 

 per cent. But if this light, already partially polarized, be transmitted through 

 other refracting surfaces, though it will continually lose in total intensity by 

 reflection, it will gain in the jjroforiion of the polarized light which it contains; 

 and if the incidence is that of the polarizing angle for reflected light, the quan- 

 tity transmitted W^ /c/i is poIa?-i zed, yv\\l continue to increase i?i absolute amount, 

 notwithstanding the decrease of total intensity, until polarized light only is trans- 

 mitted. Moreover, if the number of refracting plates employed should happen 

 to be greater than is necessary to produce complete polarization, the supernu- 

 merary plates will not reduce the amount of polarized light transmitted ; since, 

 at the incidence supposed, they are incapable of reflecting light polarized trans- 

 versely to the plane of reflection. This statement presumes, of course, that 



