Jan. I, 1874J 



NA TURE 



167 



POLARISATION OF LIGHT* 

 II. 



THE experiment described in the previous article, in 

 which the rays reflected from the pile of glass plates 

 are extinguished by the analyser when in one position, 

 while those which have been transmitted are extinguished 

 when the analyser is in a position at right angles to the 

 former, shows that the vibrations of the reflected and 

 refracted rays, so far as they become polarised, are at 

 right angles to one another. And further, if these rays 

 be severally examined with a plate of tourmalin, it will be 

 found that the vibrations of the reflected ray are executed in 

 a direction perpendicular to the plane of incidence, and 

 those of the refracted ray in a direction parallel to that 

 plane. 



The same general reasoning as that used in the case of 

 tourmalin plates will serve, if not as actual proof, at all 

 events as illustration in this case. Thus, suppose that a 

 ray whose vibrations are perpendicular to the plane of 

 incidence, that is, parallel to the reflecting surface, fall 

 upon a plate of glass ; then there is no apparent reason 

 why a change in the angle of incidence should modify 

 the reflection and refraction, so far as they depend directly 

 upon the direction of the vibrations. The vibrations 

 cannot undergo any change of direction on one side 

 rather than on the other by incidence on a surface to 

 which they are parallel, and will consequently remain 

 parallel to themselves even when the incidence has taken 

 place. And since the reflected and refracted rays both 

 lie in the plane of incidence, the vibrations (which are 

 perpendicular to that plane and consequently to every 

 line in it) will fulfil the optical condition of being perpen- 



FlG. g. 



dicular to the rays in question. But if the vibrations 

 of the incident ray take place in the plane of incidence, 

 it is diliicult to conceive that the results of reflection and 

 refraction should be unaffected by a change in the angle 

 of incidence. There are two mathematical and mecha- 

 nical principles which, when applied to the case of vibra- 

 tions in the plane of incidence, lead to the conclusion that 

 if the ray be incident at such an angle that the reflected 

 and refracted rays are perpendicular to one another, there 

 can be no reflected ray. 



A general explanation of this very curious result seems 

 dil'ficult ; but the following considerations may perhaps 

 tend to elucidate the subject. Reflexion is generally, 

 perhaps always, accompanied by refraction. Bodies are 

 visible in virtue of rays which, after reflexion from their 

 surface, meet the eye. But the natural colours of bodies 

 so seen are due to rays which are not reflected until they 

 have penetrated to some, although inconsiderable, depth 

 below the actual surface. During this penetration the 

 light has been deprived of certain of its component rays, 

 and emerges as a reflected beam covered with the remain- 

 ing or complementary tint. And although the colourless 

 reflexion from polished surfaces is an apparent exception 

 to the rule, it may still be the fact that this is only a 

 limiting case in which the penetration is a muiimum. If 

 this be so, we may fairly conclude that refraction is the 

 ruling feature of the phenomenon, and that it in some 

 sense precedes reflexion. With the change of direction 



* Coiiunued Trom p. i--_). 



of the ray involved in refraction it is in the highest degree 

 probable that a change of direction of the vibrations 

 (supposed always to be in the plane of incidence) will be 

 also involved. The simplest supjosition would be that 

 the vibrations within the medium are perpendicular to the 

 refracted ray ; and that the intensity of the reflected light 

 is due to that part of them which can be resolved in a 

 direction perpendicular to that of the reflected ray. If, 

 therefore, the refracted and the reflected rays be perpen- 

 dicular, so also will be their vibrations, and consequently 



no part of the vibrations constituting the former can be 

 resolved in the direction requisite for the latter. In other 

 words there will be no reflected ray. 



The above remarks give, it must be admitted, no me- 

 chanical theory of reflexions, nor indeed do they pretend 

 to be even a rough explanation of the facts. They merely 

 amount to this : If reflexion depends primarily upon re- 

 fraction, and the known law of reflexion obtains inde- 

 pendently of all questions of polarisation, then when the 

 incident vibrations take place in the plane of incidence 

 no reflected ray, whose direction is perpendicular to that 

 of the refracted ray, can be produced. 



We next come to the subject of polarisation by double 

 refraction. There are a large number of crystals which 

 have the property of generally dividing every ray which 

 passes through them into two. But the extent of separa- 

 tion of the two rays varies with the direction of the inci- 

 dent ray in reference to the natural figure of the crystal. 



In every double refracting crystal there is at least one, 

 and in many there are tv/o, directions in which no such 

 separation takes place. These directions are called optic 

 axes. The relations betvveen the forms of crystals and 

 their optic axes, and optical properties arising there.'rarn, 

 will be explained later. 



Of such crystals Iceland spar is the most notable in- 

 stance. If we take a block of such spar split into its 

 natural shape, a rhombohedron. Fig. 9, and for conveni- 

 ence cut off the blunt angles by planes perpendicular to 

 the line joining them, a b, it will be seen that a ray of light, 

 transmitted perpendicularly to these planes, that is 



