138 TOTAL REFLECTION ELLIPTIC POLARIZATION. 



can be uo emergent ray; and hence tlna is called the Ihniiing angle. For all 

 incidences from j to 90° the whole of the light is reflected; and this is what is 

 meant by total rfficction at second surfaces. 



Mr. Fresnel found that the mathematical formirloj which he had deduced from 

 his theory of light, to express the intensity of reflection at different incidences, . 

 became imaginary in the case of total reflection ; and in reasoning on the prob- 

 able causes of their failure, he was led to predict that a rhomb of glass, having 

 the angles above stated, would produce precisely the efi'ect which has just been 

 described. Experiment proved the truth of this anticipation. The nature of 

 the modification which light undergoes in these circumstances will be more fully 

 explained further on. 



Reflection from metals presents characters which resemble those of reflection 

 from the second surface of transparent media. There is this difference : that 

 common light totally reflected exhibits no traces of polarization; but common 

 light reflected from metallic surfaces is partially polarized. When the incident 

 light at second surfaces is polarized in an azimuth bi'tween 0° and 90^^ the modi- 

 fications which it undergoes lescmblc those produced by metals. This subject 

 was fi.st systematically investigated by Sir David Brewster. He first discov- 

 ered that polarized light, after having unde:gone one total reflection in an azi- 

 muth between 0'^ and 90°, produced colors, when examined with an analyzer, 

 analogous to those produced by thin crystalline laminae. He afteiwa.ds ascer- 

 tained that a polarized ray which has undergone successive reflections from 

 phme metallic mirrors placed parallel to each other, when the original azimuth 

 of reflection is 45° from the plane of polarization, will exhibit similar tints. 

 Th" angle of incidence at which the effect is best produced varies with different 

 metals, but is in all, or nearly all cases, above 70° and below 80". The biight- 

 ness of the tints increases with the number of reflections. 



Sir David B.ewstei' also found this analogy between the effects of such a pair 

 of parallel metallic mirrors and a pair of Fiesnel's rhoinbs : that at a ce. taiu 

 angh of incidence, different for different metals, the effect of the reflection on 

 the first mirror would be exactly compensated by that on the second, and the 

 ray would emerge plane polarized. But he found also this difference between the 

 ca-=es : that while (the azimuth of incidence being + 45°) the ultimate plane of 

 polarization with the rhombs was — 45°, that with the metallic mirrors was 

 always less than this, being for silver, in which it was greatest, — 39° 48', and 

 for galena, in which it Avas least, no more than — 2°. There is also this addi- 

 tional and very remarkable difference : In the case of the rhombs, after the 

 light has undergone reflection in the first, it will be restored to its original con- 

 dition by the second, no matter what be the azimuth between the planes of 

 reflection in the two rhombs. But in the case of the mirrors, if the second be 

 turned in azimuth, it will no longer restore the ray, unless the angle of incidence 

 be changed also. If it be turned quite roimd, the angle of incidence required 

 to effect restoration will pass through a series of regular variations between 

 determinate limits, which variations may be represented by the varying radii of 

 an eDipse. It was on this account that the term elliptical polarization was 

 originally applied to light in this physical condition. We shall see, further on, 

 that the propriety of the term may be established on other grounds. 



Common light reflected from metallic surfaces is more or less elliptically 

 polarized. In fact, the recent investigations of Mr. Jamin and others have 

 proved that there are very few substances which furnish by reflection from their 

 surfeces absolutely pure plane polarized light. None are capable of doing so 

 whose indexes 'of r(-fraction excised or fall short of 1.414. Water and glass do 

 Bo sensibly; but in this respect they arc nearly exceptional. 



