POLARIZATION OK LIGHT. 



POLARIZATION OK l.HillT. 



seo 



rhomb with which he was furnished when the latter rhomb was turned 

 till the extraordinary pencil disappeared. 



Light pound rig the properties which hare just been described as 

 belonging to the ordinary ray in a rhomb of Iceland spar, however 

 those properties may have been acquired, is said to be pvlariitd, and 

 the plane to which the properties are related as are those of the ordinary 

 ray to the principal plane of the crystal is called the jJaitf uf polariza- 

 tion. The polar-nation may be detected, and the azimuth of the plane 

 of polarization determined, by means of a rhomb of Iceland spar, as 

 above described. 



The properties of a ray which emerges after extraordinary refraction 

 in a rhomb of Iceland spar, as may be inferred from the description 

 given above, are absolutely identical with those of the ordinary ray, 

 except that they are similarly related to a plane perpendicular to the 

 principal plane. Hence the extraordinary ray is polarized in a plane 

 perpendicular to the principal plane, the ordinary ray being, according 

 to our definition, polarized in the principal plane. 



If a piece of Iceland spar, or other doubly refracting crystal, be cut 

 into the form of a wedge or prism, the deviation of the two rays, into 

 which a ray incident upon it is in general divided by double refraction, 

 will not be the same, and thus the rays will emerge in directions 

 inclined to each other, BO that their lateral separation will increase 

 with the distance from the prism. Two such rays are still found to 

 be polarized, and their planes of polarization to be nearly perpendicular 

 to each other, being accurately so when the refracting edge is per- 

 pendicular to a plane of optical symmetry, or principal plane, of the 

 crystal, and the refraction takes place in that plane. 



Kor more than a century after the original discovery of Huygens, 

 double refraction was the only phenomenon in which light was known 

 to receive the modification called polarization. But in the year 1808, 

 Malus made the important discovery that light receives the same 

 modification by reflection at a certain angle from the surface of glass, 

 water, and transparent substances in general, provided their surfaces be 

 smooth or polished, so as to give a regular reflection. The plane of 

 reflection was found to be the plane of polarization of light thus 

 polarized. The angle of incidence required for complete polarization 

 by reflection waa found to vary with the nature of the substance. At 

 an angle of incidence greater or less than this (but not reaching 

 0* or 90) the same modification was imperfectly produced, the light 

 never vanishing on rotating the analysing rhomb, but only passing 

 through a minimum in those positions in which at the polarizing angle 

 it vanished altogether. The simplest conception to form of the nature 

 of light thus partially polarized ia to regard it as a mixture of common 

 light and of light polarized in the plane of incidence. The refracted 

 light is found to be only partially polarized even at the angle of com- 

 plete polarization of the reflected light, the plane of polarization being 

 perpendicular to the plane of incidence. It may be regarded as 

 composed of a mixture of common light and of light polarized in the 

 plane last mentioned ; and.it has been found that at the same angle of 

 incidence the quantity of light polarized in thn plane of incidence 

 contained in the reflected beam is equal to the quantity of light 

 polarized in the perpendicular plane contained in the refracted beam. 

 When common light is reflected from a metal, the reflected light is 

 only partially polarized in the plane of incidence, whatever be the 

 angle of incidence. 



Shortly after Malus's discovery of the polarization of light by 

 reflection, Sir David Brewster commenced an extensive series of expe- 

 riments on the polarizing angle of a variety of media, which resulted 

 in the discovery of the beautiful law which determines the angle of 

 polarization, namely, that the tangent of the polarizing angle is equal 

 to the index of refraction, which may be otherwise expressed by saying 

 that the angle requisite for complete polarization is that for which the 

 directions of the reflected and refracted rays ore perpendicular to each 

 other. This law embraces, as a particular cose, a law which Malus 

 had already found, that when light is incident on a plate of glass or 

 other medium bounded by parallel surfaces at the angle required for 

 complete polarization of the light reflected at the first surface, the 

 refracted light is also incident on the second surface at the angle of 

 polarization for internal reflection. Accordingly a plate of glass, or a 

 pile of plates, may be used instead of a single surface to furnish 

 polarized light by reflection at the proper angle, and a pile of plates 

 has the advantage of giving light of much greater intensity than would 

 be got from a single surface. 



Certain doubly refracting crystals have the property of absorbing 

 vary unequally the oppositely polarized pencils into wliii h tlu-y !;*:.; 

 an incident peticil of common light. Thus certain varieties of 

 tourmaline, cut Jiorallel to the axis of the crystal, when of a certain 

 thickness, absorb almost completely the ordinary ray, and transmit a 

 great portion of the extraordinary. Hence the light transmitted by 

 such a plate is almost perfectly polarized, in a plane perpendicular to 

 the axis of the crystal, and the plate may be used either for procuring 

 polarized light in the first instance, or for examining light already 

 polarized. 



The general phenomenon of the relation of the properties of a 

 polarized beam to directions transverse to the beam may be studied 

 very simply in the case of polarization Ijy reflection. It i miflic.icnt. to 

 mount tyv<> pieces of glass, blackened at the back, so that tin- line 

 joining their middle points is inclined approximately ;it thv polarizing 



angle (about 54* 85') to the surface of each, and that one of them is 

 moveible about that line as an axis. The light of the clouds is 

 reflected from the first glass on to the second, and from then. into the 

 eye, which must follow the light in the rotation of the glass. V 'In n 

 the planes of reflection coincide, the light is copiously reflected, I ait 

 on turning the moveable glass on its axis the Intensity ilimi- 

 until on turning to !iO, when the planes of reflection bee 

 dlcular to each other, a dark cloud is seen about the , 

 fiYM. tliu mill. II.- of which in perfectly black when tin- adji^' 



rfect, or at least would be so with h, -: li^ht. The 



experiment may even be performed by using the 1 ..My 



reflection from a polished table, and examining it with a I it of gloss, 

 blackened at the back, which is held in the hand. In 

 splendid colours given, as will presently be mentioned, by thin 

 of selenite, ftc., may be seen perfectly well, by merely 'holding the 

 plate in the path of the light incident upon the moveable mirror. 



In any combination consisting of apiece (suppose a pile of i 

 which may be called the polarizer, destined to furnish ],l.iii/cd light 

 in the first instance, and of a piece (suppose a tourmaline or a N 

 prism), destined to examine the light furnished by th 

 whether modified or not in its passage to the analyzer, if the an 

 be turned till the light is extinguished, and a rhomb of Icclan 

 i- introduced between the polarizer and analyzer, and be turned round, 

 the light will in general be found to be more or less restored. 1 

 rectangular positions of the rhomb, namely, when its principal j 

 parallel or perpendicular to the plane of priinit 



the plane of polarization of the polarized light incident on the rhomb), 

 no effect is produced, and the field remains dark. But the moment 

 the rhomb is turned from any one of these positions the light begins 

 to reappear, and increases in intensity till the rhomb lias turned 45 

 from the vanishing position, after which it again decreases by the same 



M. 



The nature of the restoration may be analyzed by placing a screen 

 with a small hole on the face of the rhomb by which the light enters, 

 so as to separate the emergent pencils. As these are polarized in 

 planes depending, not on the plane of primitive polarization, but on 

 certain directions fixed in the rhomb, and therefore no longer perpen- 

 dicular to the plane of polarization of the analyzer, they ore each jui - 

 tially transpiitted by the analyzer. If the hole be now made larger, 

 the partially transmitted images will overlap, and if the screen be 

 taken away altogether the light perceived must still be regarded as a 

 mixture of two neams, the ordinary and extraordinary respectively of 

 the rhomb, each partially transmitted by the analyzer. 



When a beam of polarized light is divided into two, polarized in 

 rectangular planes, by a rhomb of Iceland spar, the intensity of i 

 beam was assumed by Malus to vary as the square of the cosine of 

 the inclination of its plane of polarization to the plane of primitive 

 polarization, A law which was afterwards verified experimentally by 

 Arogo, and which applies equally to reflection from glass at the | 

 izing angle, the angle between the plane of reflection from the glass 

 and the plane of polarization of the light incident upon it being now 

 that of which the squared cosine varies as the intensity of the reflected 

 light. If then, in our supposed experiment, the rhomb be turned till 

 its principal plane is inclined at an angle j to the plane of primitive 

 polarization, and if the intensity of the incident polarized light IK) 

 taken as unity, the intensities of ordinary and extraordinary beams 

 will be 'expressed by cos* i, and cos 5 ( i + 90 ), or sin- ', respec- 

 tively. As the planes of polarization of these beams are inclined at 

 angles 90 i and i respectively to the plane of polarization of the ana- 

 lyzer, the fractions of the beams transmitted by the analyzer will bo 

 measured by sin 2 i, cos j i, respectively, so that the whole intensity 

 will be measured by coa't sin- i + nm-i, cosf, or ^ thr'2l, which 

 vanishes when i= 0, or = 90, Ac., and has its maximum value i when 

 i = 45, or = 135, &c. 



This restoration of light which has been described in the case of 

 Iceland spar is manifested by doubly refracting crystals in gc 

 and forms a very simple and delicate test of the existence of double 

 refraction, which may be applied when, from the feebleness of tin- 

 doubly refracting power or the thinness of the crystalline plate, it 

 would be difficult or impossible to make out a separation of the in 

 It may easily be observed by using sulphate of lime or sulenite, a 

 common mineral, which has a t cleavage in one direction. 



But if the plate of selenite be very thin, nut BO thin however but 

 that such a plate may be readily obtained by cleavage, a new and splen- 

 did class of phenomena make their appearance, as was discovered by 

 Arago. In those positions in which a thick plate simply restores a 

 portion of the light, a thin plate ia seen arrayed in gorgeous colours, 

 changing with every change of thickness, and varying too when the 

 plate is considerably inclined. If the plate be fixed, and the an 

 be mode to revolve, the colours change in a remarkable n 

 win -n the rotation amount* to 90 the original colour at any ]>< 



1 by its complementary, so that the two superpo > .1 make white 

 light. This law is found to hold good for any two azimuths of the 

 analyser separated by 90, and not merely for the azimuths 



It would pass the limits of this article to describe the pin nonirn:i 

 of the colours of crystalline plates in all their details, and the still 

 more curious and complicated coloured rings of curves seen about the 



