CIECULAE POLARIZATION FRESNEL 8 RHOMB. J37 



velocities differ, but wliicli pursue the same path, which is the axis. At the 

 surface BF their paths become different, tlie velocity of 011 e of them passing 

 from — to + , and that of the other from + to — . At th(5 surface VD this 

 divergency is increased, the velocities again interchanging their relations. At 

 final emergence from the face CD, the- divei-gency will be further slightly 

 increased in consequence of the inclination of the emergent rays to the surface. 

 By this arrangement a sufficient separation of the two. rays is obtained to make 

 it possible to examine them singly. And it is obvious that a duplication of the 

 system of prisms here shown, or a still greater increase in the number of ele- 

 ments employed, would, if necessary, make the separation still wider. 



If quartz were like other uniaxial crystals in the law governing refraction 

 along its axis — that is, if the velocities of the two rays were in that direction 

 equal in this crystal as they are in others — the system of prisms just described 

 would produce no separation of the rays. The fact of the separation proves 

 quartz to be in this respect an exceptional case. When the separated rays are 

 examined, however, the extent to which quartz is exceptional is discovered to 

 be much greater than is implied in the difference just indicated. The peculiari- 

 ties are the following, and are true of either of the separated rays. 



Examined with a doubly refracting prism, two perfectly equal images appear 

 in all azimuths of the prism. Received upon a mirror at the polarizing angle, 

 equal reflection takes place in all azimuths of the mirror. In these respects the 

 rays resemble ordinary unpolarized light. 



But in the follov/ing particulars they differ : Transmitted through thin crys- 

 talline plates they display, on being analyzed, tints like those produced by 

 polarised light, only they are such tints as ordinary polarized light produces in 

 thicknesses of crystal greater or less, by a determinate amount, than those used 

 in the experiment. 



Transmitted through a rhomb of glass, like that represented 

 in the figure, of which the acute dihedral angles ai'e 54|', they 

 emerge, after two internal total reflections, at Q and P, polar- 

 ized in planes, one in azimuth 45° on the right, and the other 

 in azimuth 45*^ on the left, of the plane of reflection. If both 

 Qf^ / are transmitted through the rhomb simultaneously, so as to 



/ I / emerge together, they will form a single ray polarized in the 



JE \o plan:- of reflection. 



T"* Bays in this condition are said to be circularly polarized 



Firr. il. And as it appears that a circularly polarized ray becomes /jZa;^,? 



polarized by two internal reflections in glass, at an angle of incidence of 54° 3u', 

 the resultant plane of polarization being in azimuth 45" from the plane of reflec- 

 tion, it follows that a plane polarized ray may be circularly polarized by caus- 

 ing it to make two similar reflections, the plane of its original polarization being 

 45-' in azim.uth from that of the first reflection. This is effected by the use '>f 

 a rhomb such as has been just described, and Avhicb, from its originator, has 

 been called Fresnel's rhomb. It is obvious that, if a plane polarized ray be 

 thus passed through two of Fresnel's rhombs successively, it will emerge plane 

 polarized. 



Mr. Fresnel was led to the discovery of the remarkable property of th-; 

 rhomb which bears his name, by theoretic considerations. When light is pass- 

 ing from a denser to a rarer medium, the, angle of refraction is greater than the 

 angle of incidence, and the law of Snellius, 



sin: 

 sin,o 

 gives a value for n, the index of refraction, less than unity. Noav as 1 is the 

 greatest possible sine, if we put sin,o = l, we shall have sin£=:w; and there- 

 fore £ itself less than 90*^. For an incidence greater than this value of : there 



