May 30, 1872] 



NATURE 



91 



O^ 



ON OPTICAL PHENOMENA PRODUCED BY 

 CRYSTALS SUBMITTED TO CIRCULARLY 

 POLARISED LIGHT* 



)N a former occasion I exhibited some phenomena Jepcnciing 

 upon circular, or, as it was then also called, successive 

 P° arisition, and in particular I adopted and explained a method 

 for producing circularly polarised light devised by Sir Charles 

 Wheatstone. I propose on the present occasion to puisue 

 the s'lbject into some of its ulterior consequence?. In terms of 

 the wave theory, light is said to be circularly polarised when the 

 vibrations arc circular, as distinguished from plane polarisatio', 

 when they are rectilinear. And further, it is known from me- 

 chanical principles that a circular vibration may alivays be pro- 

 duced by the combination of two rectilinear vibrations, the am- 

 plitudes or extents of which are equal, and whereof one is in 

 advance or in rear of the other by one or by any odd number of 

 quarter-wave lengths. In the former of these cases the circular 

 motion will lake place in one direction, say right-handed, in the 

 latter in the opposite, say lef: -handed. The contrivance used for 

 producing circular polarisation this evening is known by the 

 name of a " quarter undulation plate," and consists of a plate of 

 mica split to such a thickness that one of the two rays into which 

 plane polarised light is divided on entering it is retarded by an 

 odd nunib?r of quarter-wave lengths behind the other. 



The optical phenomena produced by crystals when submitted 

 to polarised light are usually divided into two classe-, viz. ( i ) 

 those arising from the use of parallel light, and consisting of 

 broad sheets of colour ; and (2) those due to convergent I'ght, 

 and consisting of the rings and brushes, the general character of 

 which is well known. I propose to take a few specimens from 

 each cla^s, and to examine the modifications which the Ino.vn 

 phenomena undergo when the light is both polarised and analysed 

 circularly, i.e., when one quarter-undulation plate is interposed 

 between the polariser (Nicol's pri-m) and the crystal to be 

 examined, and the second between the crystal and the analjser 

 (Nic il's prism). 



In the first place, it is known that if a plate of seleniie be 

 placed in an ordiniry apparatus when the polariser and 

 analyser are either parallel or crossed, there are four positions at 

 90° apart ia which ihe plate will produce colour ; and farther, 

 that if th= analyser be turned throjgh 90° the same result will be 

 obtained, except that the colour will be complementary to that 

 first se?n. The intensity of the bght at any given point is tlien 

 given by the form da : 



,. , . ., e 



cos.-y— sin. 2 ; sin. 2\i — s) sin.- ^ 



where / and s are the angles made with the original plane of 

 polarisation by the principal sections of the crystal and of the 

 analvser respectively, and is the retardation. 



If, however, the two quarter-undulation plates (say the plates 

 A and B) be inlroduced, the light undergoes the following 

 processes : — First, it is plane polarised by ihe polariser ; 

 secondly, the plate A being placed so that its axis is inclined at 

 ± 45° to the original plane of polarisation, the light undergoes 

 right or left-handed circular polarisation, and in that condition 

 falls up jn the crystal ; thirdly, in their passage through the 

 crystal C the rays are eich divided into t.vo, whose vibrations 

 are at right angles to one another, and whereof one is retarded 

 in proportion to the thickness of C ; fourthly, the plate B being 

 placed so that its axis is parallel or perpendicular to that of A, 

 each of these sets of rays is circularly polarised, one set right- 

 handed, and the other setleft-handed ; fifthly, thesetwo oppo itely 

 circularly polarised sets of rays combine, according to known me- 

 chanical laws, on emerging from B into planerays, in which the planes 

 of polarisation of the different colours of the spectrum are turned 

 through different angles. Hence finally by turning the analyser 

 round we shall cross these various planes in turn and successively 

 extinguish the different colours, leaving the complementary 

 colours visible. The system of plates S. C E consequently acts 

 in this respect like quaitz. It is, however, to be observed that if 

 the plate B be turned from one of the two proposed positions to 

 the other, the directions of motion in the two emergent circularly 

 polarised rays, and consequently the planes of polarisation of 

 the different colours, will be reversed ; in other words, with the 

 plate B in one position we shall imitate a right-handed, with the 



* Lecture delivered at l^e Roial Institution of Great Britain, Maya, 

 1872, by W. Spolliswoode, Treas. R.S. 



plate B in the other a left-handed, quartz The intensity of the 

 fight at any point is then given liy the formula : — 



sin.-- for one position, 



cos. - - - for the other. 

 2 



Again, if the plates A B retaining either of the positions 

 before indicated, the crystal C be turned round in its own plane ; 

 then, since the light emerging from A and B is circularly 

 polarised, it has lost all trace of direction with reference to the 

 positions of the polariser and analyser, and consequently no 

 change of tint will be observed. The same is abundantly clear 

 from the formula written above, b^caufe the only term it con- 

 tain; depends upon the retardat;on within the crystal C. This 

 experiment was made by Airy. 



If the plates A and B have their axes directed 45° on either 

 side of the axis of C, and the three plates be turned round as one 

 piece, the colour will remain unchanged ; while, if the analyser 

 be turned, we have the colours shown in the regular order. If 

 the plates A and B have their axes directed at 45° on the same 

 side of the axis of C, and the pieces be turned round bodily as 

 before, the colours change in the same order as above, and go 

 through their cycle once in every 90° of rotation ; arid if the 

 analyser be turned in the same direction the colours change, but 

 in the reverse order. The explanation of this is to be found in 

 the f.ict that when the plates A and B are crossed, the retarda- 

 tion due by .\ is co-npensated by that due to B ; so that the only 

 effective retardation is that due to the crystal C. But upon this 

 depends the rotation of the plane of polarisation ; if, therefore, 

 the polariser and analyser remain fixed, the colour will remain 

 unaltered. When the plates A and B hive their axes parallel, 

 there is no compensation, and the colour will consequently 

 change. This experiment was made by Fresnel. The mathe- 

 matical expressions for the intensity of the light in the two cases 

 respectively are : — 



cos.-/y I- / -f --Y anl co3.= (j - i - - V 



where / is the angle made by the principal sections of A with 

 that of the polariser, and/ that of the principal section of B with 

 that of the analyser. The first expression is obviously unchanged 



when the angle between the polariser and analyser, viz. — -)-;'■(- y, 



is unchanged. 



It should be added that the rotation of the plane of polarisa- 

 tion, anrl consequently also the sequence of tints, does not follow 

 exactly the same law ia the above cases as in quartz. 



We now come to the case of convergent light, that is, to the 

 phenomena of crystal rings. And let us examine the effects pro- 

 duced by the same arrangement as before, viz., two quarter- 

 undulation plates, A, B, one in front and one liehind the crystal 

 C. To quote from Mr. Airy : — "The first thing that strikes us 

 in this combination is that there is nothing, except in the crystal, 

 that has any respect to sides. For the only incident light is 

 circularly polarised ; the only light allowed to emerge is circu- 

 larly polarised. The appearance, therefore, of the coloured rings, 

 &c. , must be such as conveys no trace of any plane of polarisa- 

 tion, and mu.,t not vary as the crystal is turned round. In the 

 common exhibition of the coloured rings the jirincipal trace of 

 the planes of polarisation is in the uncoloured brushes. In 

 uniaxal crystals they form an eight-rayed star, composed of two 

 square crosses, inclined at an angle eqml to that between the 

 planes of polarisation, every ray of which separates complemen- 

 tary rings. In biaxal crystals they compose two pairs of rectan- 

 gular hyperbolas, the angle between whose asymptotes is the 

 same as that between the planes of polarisation, and whose 

 branches divide complementary rings. The two crosses or two 

 sets of hyperbolas unite when the planes of polarisition are 

 parallel or perpendicular. But in the case under consideration 

 the rings exhibited by crystals will not be traversed by any 

 brushes. Uniaxal crystals will exhibit circular rings without a 

 cross ; and biaxal crystals will exhibit complete lemniscates, 

 without any interruption from curved brushes." And it is fur- 

 ther to be noticed, as the formula given above indicates, that the 

 centres of the rings will be bright or dark according as the 

 analyser stands at o" or 90°. 



To pursue this matter further. Suppose that, the arrange- 

 ments remaining otherwise as before, the analyser be turned 

 round ; then in any position intermediate to 0° and 90° the rings 



