CHAPTER V.

CIRCULAR POLARISATION BY REFLEXION.

THE conversion of plane into circularly polarised light may also be effected by total reflexion. If planepolarised light traversing glass be incident upon the inner side of the limiting surface at any angle at which total reflexion takes place, it may be considered as resolved into two plane-polarised rays, the vibrations of one being parallel and those of the other perpendicular to the plane of reflexion; and there is reason to believe that in every such case a difference of phase is brought about which for a particular angle in each substance (in St. Gobain glass it is 54° 30') it has a maximum value somewhat in excess of one-eighth of a wave length. There are two angles, one on each side of that giving the maximum, for which the difference of phase is one-eighth of a wave length. And if the original plane of vibration be inclined at an angle of 45° to that of reflexion, the amplitudes of the two vibrations, into which the reflected vibrations are supposed to be resolved, will be equal. A full discussion of the mechanical causes which may be considered to effect this difference of phase would carry us deeper into the more

difficult parts of the Wave Theory than would be suitable in this place. But if we accept the fact that the above-mentioned effects result, when polarised light (whose plane of vibration is inclined at 45° to that of reflexion, so as to ensure an equality of amplitudes in the components) is reflected at a proper angle, then the following construction will be readily understood. Take a rhomb of glass, a, b, c, d, Fig. 14, whose acute angles are 54° 30'; a ray incident perpendicularly to either end will undergo two total internal reflexions at the sides-say at p and s-and will emerge

P

FIG. 14.

perpendicularly to the other end.

These two reflex

ions will together produce a retardation, as described above, of one-fourth of a wave length. And if the ray be originally polarised, and its plane of vibration be inclined at an angle of 45° to that of reflexion (that of the paper in the figure), the amplitudes of the two vibrations will be equal; and all the conditions will be fulfilled for the production of circular polarisation. Such an instrument was invented by Fresnel, and is called in consequence Fresnel's rhomb. On account of its length and its displacement of the ray,

it is not so convenient as a quarter-undulation plate; but, on the other hand, it affects rays of all wave lengths equally, while the quarter-undulation plate can strictly be adapted to rays of only one wave length.

If either of these instruments be introduced and suitably placed between a selenite plate and the analyser, the chromatic effects will be similar to those due to a plate of quartz cut perpendicularly to the axis.

Another important property of these instruments consists in their effect upon circularly polarised light. Such light may be considered as arising from two plane-polarised rays whose vibrations are perpendicular to one another, and which present a difference of phase equal to a quarter of a wave length. If, therefore, either a quarter-undulation plate or a Fresnel's rhomb be suitably placed, it will either increase or diminish the difference of phase by a quarter of a wave length. In the one case the difference of phase will amount to a half-wave length, in the other it will vanish. And in either case the vibration will be converted into a rectilinear one; but the directions of vibration in the two cases will be perpendicular to one another.

Some years ago Sir Charles Wheatstone devised a very beautiful application of reflexion from a metallic surface for converting plane into circular, or, as he termed it, successive, polarisation. The following is a sketch of the principle upon which it is based. If a ray of plane-polarised light fall upon a metallic reflector, it is divided into two, whose vibrations are respectively parallel and perpendicular to the reflector; and the latter is retarded behind the former by a difference of phase depending upon the angle of

incidence. If the plane of vibration of the incident ray be inclined to the plane of incidence at an angle (nearly 45°) which varies with the metal employed, but which is perfectly definite, the intensities become equal. And further, if the angle of incidence have a particular value, dependent upon the nature of the metal (for silver 72°), the retardation will amount to a quarter of a wave length. And the result will be a circularly polarised ray, as in the case of total reflexion.

To give practical effect to the use of this principle, the author of it modified the construction of Norremberg's polariscope so as to admit of the introduction of a silvered plate in a proper position. The following description is quoted from his paper on the subject (see Fig. 15).

"A plate of black glass, G, is fixed at an angle of 18° to the horizon. The film to be examined is to be placed on a diaphragm, D, so that the light reflected at the polarising angle from the glass plate shall pass through it at right angles, and, after reflexion at an angle of 18° from the surface of a polished silver plate S, shall proceed vertically upwards. N is a Nicol's prism, or any other analyser, placed in the path of the second reflexion. The diaphragm is furnished with a ring, movable in its own plane, by which the crystallised plate to be examined may be placed in any azimuth. C is a small movable stand by means of which the film to be examined may be placed in any azimuth and at any inclination; for the usual experiments this is removed.

"If a lamina of quartz cut parallel to the axis, and sufficiently thin to show the colours of polarised light,