CHAPTER IX. ROTATORY POLARIZATION. 146. WHEN plane polarized light is transmitted at normal incidence through a plate of Iceland spar, which is cut perpendicularly to the axis, the plane of polarization of the emergent light coincides with that of the incident light. It was however discovered by Arago' in 1811, that there are certain uniaxal crystals, of which quartz is the most notable example, which possess the power of rotating the plane of polarization. It thus appears, that crystals of the class to which quartz belongs possess certain peculiarities, which distinguish them from ordinary uniaxal crystals, such as Iceland spar. The subject of the rotation of the plane of polarization by crystals was afterwards studied experimentally by Biot', who established the following laws. I. The rotation of the plane of polarization produced by a plate of quartz cut perpendicularly to the axis, is directly proportional to the thickness of the plate, and inversely proportional to the square of the wave-length of the particular light employed. II. If an observer looks along the direction in which the light is travelling, there are certain varieties of quartz which rotate the plane of polarization towards his right hand, whilst there are others which rotate it towards his left hand. The former class of crystals are called right-handed, and the latter left-handed. 1 Mém. de la prem, classe de l'Inst. vol. xii. p. 93; see also Euvres Complètes x., p. 36. 2 Mém. de l'Acad. des Sciences, vol. 11. p. 41. From this definition it follows, that if an observer, who is looking through a Nicol's prism at a ray of plane polarized light, places the Nicol in the position of extinction, and then inserts a plate of right-handed quartz, he must turn the Nicol towards his left-hand in order to bring it into the position of extinction; whilst if the plate of quartz is left-handed, he must turn the Nicol towards his right. Many continental writers adopt a definition, according to which, a plate of quartz is considered right-handed, when the observer has to turn his Nicol towards the right, in order to bring it into the position of extinction; but I have decided after much consideration, to adopt a definition, in which the directions of propagation and rotation are related in the same manner, as the magnetic force produced by an electric current circulating round the ray. 147. Since the rotation varies inversely as the square of the wave-length, the position of the plane of polarization will be different for different colours. If sunlight be employed, the different colours will be superposed on emergence, and the emergent light will be white; but if the emergent light be examined by a Nicol's prism, placed so that its principal section is parallel to the plane of polarization of any particular colour, that colour will be extinguished, and the light on emergence from the Nicol will appear coloured. The following table gives the values found by Broch', for the rotations of the principal lines of the spectrum, produced by a plate of quartz one millimetre in thickness. From this table it appears that the law, that the rotation is inversely proportional to the square of the wave-length, is only approximate. 1 Ann. de Chim, de la Phys. (3), xxxiv. p. 119. QUARTZ AND MAGNETIZED MEDIA. 159 148. On account of the smallness of the wave-length of all visible parts of the spectrum, it follows from the first law, that the rotation will amount to a large number of right angles, if the thickness of the plate is considerable. Unless therefore the plate is sufficiently thin for the rotation to amount to less than 180°, the observer is liable to be mistaken as to whether the direction of rotation is to the right or to the left. In fact it appears from the table, that for the line G of the spectrum, a plate of quartz only one millimetre in thickness produces a rotation of 42° 12′. By employing plates of different thicknesses all cut from the same specimen of crystal, or by employing light of different colours, all chances of error can be eliminated. 149. The photogyric properties of quartz depend upon the angle which the ray traversing the crystal makes with the axis; they are most marked when the ray is parallel, and disappear when the ray is perpendicular to the axis; for the latter direction, quartz behaves in the same manner as Iceland spar. There are also certain liquids, such as oil of turpentine, essence of lemon, common syrup &c., which possess the power of rotating the plane of polarization of light; and this property is independent of the direction of the transmitted light. 150. Faraday' discovered, that when plane polarized light is transmitted through a transparent diamagnetic medium, which is placed in a field of magnetic force, whose direction is parallel to that of the ray, a rotation of the plane of polarization takes place; and the direction of rotation is the same as that in which a positive electric current must circulate round the ray, in order to produce a magnetic force in the same direction as that which actually exists in the medium. It was afterwards discovered by Verdet, that certain ferromagnetic media, such as a strong solution of perchloride of iron in wood spirit, produce a rotation in the opposite direction to that of the current which would give rise to the magnetic force. 151. There is an important distinction between the rotation produced by quartz, turpentine &c., and that produced by a magnetic field. If, when a ray is transmitted through quartz in a given direction, the rotation is from left to right, it is found that 1 Experimental Researches, xixth series, §§ 2146-2242. 2 C. R. vol. LVI. p. 630; vol. LVII. p. 670; Ann. de Chim, et de Phys. (3), vol. LXIX. 415; Mém, de l'Inst. vol. xxxi. pp. 106, 341. when the ray is transmitted in the opposite direction, the rotation is from right to left. If therefore the ray after passing through a plate of quartz, be reflected at perpendicular incidence by a mirror, and thus be made to return through the plate in the same direction, the rotation will be reversed, so that on emerging a second time from the plate, the plane of polarization will be restored to its original position. But when the ray is transmitted through a magnetic field, the direction of rotation in space is always the same, whether the ray is propagated along the positive or negative direction of the magnetic force; if therefore the ray be reflected, and be made to return through the magnetic field, the rotation will be doubled. The photogyric properties of a magnetic field will be more fully considered, when we discuss the electromagnetic theory of light. 152. The dynamical theories which have been proposed to account for rotatory polarization will be considered later on. At present we shall show how these phenomena can be explained by geometrical considerations. Fresnel assumed, that the only kind of waves, which media of this class are capable of propagating without change of type, are circularly polarized waves. If light polarized in any other manner is incident upon the medium, Fresnel supposed that the wave is immediately split up, on entering the medium, into two waves which are circularly polarized in opposite directions, and are transmitted with different velocities. Let us therefore suppose, that a plane polarized wave is incident normally at a point 0 upon a plate of quartz cut perpendicularly to the axis. Let the incident displacement be parallel to y and equal to a sin o, where = 2πt/T; and let the axis of z be the axis of the quartz. The incident wave may be conceived to be made up of the four displacements By 13, the displacements (u, v) represent a right-handed circularly polarized wave, while the displacements (u, v) represent a left-handed wave. Their combination is equivalent to a single plane polarized wave. FRESNEL'S INVESTIGATION. 2 161 Let d be the thickness of the plate; V1, V, the velocities of propagation of the two waves. Then on emergence, the two waves are represented by d v1 = acos2 (t−√), v, - ha sin 27 (t − ), T = = T =- ja cos(t), - ja sin 2(t); 2 We therefore see that the emergent light is plane polarized, and that the plane of polarization is rotated through an angle 2 T V1 V 27 ..(1). Hence according as V,> or < V1, the rotation will be towards the right-hand or the left-hand of a person who is looking along the positive direction of the axis of z, which is the direction in which the wave is supposed to be travelling. From this result, coupled with the definition in § 146, it follows that in right-handed quartz, the velocity of the left-handed circularly polarized wave is greater than that of the right-handed wave; whilst the converse is the case with left-handed quartz. Equation (1) is in accordance with the experimental fact, that the rotation is proportional to the thickness, but it does not give any information respecting the dependance of the rotation upon the wave-length, inasmuch as the relation between V1, V, and 7 is unknown. Experiment however shows that V1- V, must be a function of the period. 2 2 153. From the table on page 158, it follows that a plate of quartz one millimetre in thickness rotates the plane of polarization of the mean yellow rays (that is the rays midway between the lines D and E), through an angle of about 24°. Hence a plate 11 B. O. |