POLARISATION OF LIGHT. 



various magnitudes, M. Biot determined 

 that the change of polarisation of the 

 pencil E was always equal to 2 a, and 

 he thus established his doctrine of move- 

 able polarisation in a double azimuth, 

 in contradistinction to fixed polarisation, 

 or that which takes place in thick crystals. 

 Hence it follows that in thin plates the 

 pencils O and E are not polarised at 

 right angles to each other, as in thick 

 plates ; but no attempt was made to de- 

 termine by what changes the moveable 

 polarisation passed into the fixed polari- 

 sation, or at what limit a plate ceased to 

 be a thin one, or began to be a thick one. 



Upon this doctrine M. Biot attempted 

 to explain all the colours of polarised 

 light by his theory of the " oscillation of 

 luminous molecules," a theoiy of great 

 boldness and ingenuity. He " supposed 

 that as soon as a polarised ray pene- 

 trated a thin crystalline plate, its plane 

 of polarisation oscillated alternately in 

 two different planes, one its original 

 plane of polarisation, and the other the 

 plane of 2 a. The frequency of these 

 alternations, like Newton's fits, varied 

 with the refrangibility of the ray, being 

 greatest in the red and least in the violet, 

 and are supposed to take place at equal in- 

 tervals, while the ray is passing through 

 the plate. Upon this hypothesis M. Biot 

 has founded his explanation of the colours 

 of polarised light ; and it might have re- 

 mained long as a monument of the au- 

 thor's ingenuity and as a hypothetical ex- 

 pression of a great number of phenomena, 

 had not M. Fresnel sapped its foundations 

 by a beautiful analysis of the phenomena 

 on which it rests, and a reference of all the 

 colours of polarised light to the general 

 principle of interference. This explana- 

 tion, indeed, was first given by Dr. Thos. 

 Young, but it was the discovery of M. 

 Fresnel alone that established it upon an 

 impregnable basis. 



The general principle of the interfer- 

 ence of common light has been explained 

 in the Treatise on Optics, Chap. XII. 

 p. 3 1 . We shall therefore proceed to give 

 some account of the experiments of M. 

 Fresnel, who was associated with M. 

 Arago in this inquiry. The following 

 is a brief view of the leading results which 

 they obtained. 



1 . Jl'hen two rays, polarised in the 

 same plane, interfere with each other, 

 the phenomena of their interference are 

 identically the same as with two rays of 

 common light, 



This law may be easily verified by re- 

 peating the experiment in Chap. XII. 

 p. 31, in po-arised instead of common 

 light, when it will be found that the 

 fringes polarised by interference, and 

 shown in/o-. 34, are exactly the same as 

 there represented. 



2. Two rays of light polarised at 

 right angles to each other exhibit none 

 of the phenomena of interference. 



In order to prove this, M. Fresnel 

 bisected a rhomboid of Iceland spar, so 

 that each piece at the line of bisection 

 must have had exactly the same thick- 

 ness. He then placed the one above 

 the other, so that their principal sections 

 formed an angle of 90. In this state 

 the emergent pencils will only be dou- 

 ble, as shown at F,J?g. 20. These two 

 pencils, therefore, differ only in being 

 polarised at right angles to each other, 

 and when any body is placed in this light 

 no phenomena of interference are visible. 



M. Arago obtained the same result by 

 transmitting light diverging from a lu- 

 minous point through two fine slits in a 

 thin piece of copper. When these slits 

 were viewed by a lens in the manner 

 employed by Fresnel, the fringes pro- 

 duced by interference were distinctly 

 visible. "He then prepared two bundles 

 of pieces of thin mica, or films of blown 

 glass, by dividing one bundle into two 

 with a sharp cutting instrument. These 

 bundles were placed so that they could 

 revolve ; and when they were so arranged 

 as to polarise light in parallel planes, 

 distinct fringes were produced by the 

 slits, in the same manner as if the bundles 

 of mica were removed ; but when they 

 were placed so as to polarise the light in 

 rectangular planes, no fringes were pro- 

 duced. A still more elegant and con- 

 vincing experiment was employed by M. 

 Fresnel. He placed a film of sulphate 

 of lime before two narrow slits. Two 

 images of each slit were thus produced, 

 which may be called R O, R E, and L O, 

 L E, viz. light ordinary ray, right extra- 

 ordinary ray, &c., according as they come 

 from the light or left hand slit. In ob- 

 serving carefully the results of the expe- 

 riment, it is found that R O and L O, 

 and RE and L E, similarly polarised, 

 produce by their interference distinct 

 fringes ; while R O and L E, and L O 

 and R E produce no fringes at all. This 

 experiment admits of a beautiful varia- 

 tion by bisecting the film, and turning one 

 half a quadrant round in its own plane ; 



