Certain doubly refracting crystals have the property of absorbing very unequally the oppositely polarized pencils into which they divide an incident pehcil of common light. Thus certain varieties of teurtnaline, cut parallel 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 ixdarized light in the first instance, or for examining light already polarized.
The general phenomenon of the relation of tho properties of a polarized beam to directions transverse to the beam may be studied very simply in the ease of polarization by reflection. It is sufficient to mount two pieces of glass, blackened at the back, se that the line joining their middle points is inclined approximately at the polarizing angle (about 54" 35') to the surface of each, and that one of them is moveable about that line as an axis. Tho light of the clouds is reflected from the first glass on to the second, and from thence Into the eye, w !itch must follow the light in the rotation of the glass. When the planes of reflection coincide, the light is copiously reflected, but on turning the moveable glees of Its axis the intensity diminishes, until on turning to 90°, *hen the planes of reflection become perpen dicular to each other, a dark cloud is seen about the centre of the field, the middle of which is perfectly black when the adjustments are perfect, or at least would be so with homogeneous light. ThO experiment may even be performed by using the light polarized by reflection from a polished table, and examining it with a bit of glass, blackened at the back, which is held in the hand. In this way the splendid colours given, as will presently be mentioned, by thin plates of selenite, &c., 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 a piece (suppose a pile of plates), which may be called the polarizer, destined to furnish polarized light In the first Instance, and of a piece (suppose a tourmaline or a Nicola prism), destined to examine the light furnished by the polarizer, whether modified or not in its passage to the analyzer, if the analyzer be turned till the light is extinguished, and a rhoinb of Iceland spar be introduced between the polarizer and analyzer, and be turned round, the light will in general be found to be more or leas restored. In two rectangular positions of the rhomb, namely, when its priucipal plane is parallel or perpendicular to the plane of primitive polarization (that is, the plane of polarization of the polarized light incident on the rhomb), no effect is produced, and the tleld remains dark. But the moment
the rhumb is turned from any one of these positions the light begins to reappear, and increases in intensity till the rhomb has turned 45° from the vanishing position, after which it again decreases by the same steps.
Tho 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 euters, ao as to separate the emergent pencils. As these are polarized in planes depending, not on the piano 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 are each par tially transmitted 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 beams, 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 iu rectangular planes, by a rhomb of Iceland spar, the intensity of either 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 Arago, and which applies equally to reflection from glass at the polar 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 piano is inclined at an angle i to the plane of primitive polarization, and if the intensity of the Incident polarized light be taken as unity, the intensities of ordinary and extraordinary beams will be rexpressed by coal i, and cost (1+ 00°), or sin= i, respec tively. A8 the planes of polarization of these beams are inclined at angles 00°—i and i respectively to the plane of polarization of the ana lyzer, the fractious of the beams transmitted by the analyzer will be measured by respectively, ao that the whole intensity will be measured by cos'i sine i+ coati, or 8 which vanishes when i= 0, or =90°, fie., and has its maximum value when 1=45, or =135°, &c.