Light and heat are also polarized by refraction, for certain substances, especially irregularly crystallised minerals like Iceland spar, possess the property of dividing a ray of light or heat passing through them in certain directions into two pencils, namely, the ordinary and extraordinary rays. The first of these is refracted according to the same law as in glass or water, never quitting the plane perpendicular to the refracting surface, while the second does quit that plane, being refracted according to a different and more complicated law. Hence, if a crystal of Iceland spar be held to the eye, two images of the same object will generally be seen of equal brightness. But when they are viewed through a plate of tourmaline it will be found that while the spar remains in the same position the images vary in relative brightness as the tourmaline is made to revolve in the same plane; one increases in intensity till it arrives at a maximum, at the same time that the other diminishes till it vanishes, and so on alternately at each quarter revolution of the tourmaline, proving both rays to be polarized. For in one position the tourmaline transmits the ordinary ray and reflects the extraordinary, and after revolving 90°, the extraordinary ray is transmitted and the ordinary ray is reflected.
The undulations of the ethereal medium which produce the sensation of common light, are performed in every plane at right angles to the direction in which the ray is moving, but the case is very different after the ray has been polarized by passing through a substance like Iceland spar, for the light then proceeds in two parallel pencils whose undulations are still indeed transverse to the direction of the rays, but they are accomplished in planes at right angles to one another. The ray of common light is like a round rod, whereas the parallel polarized rays resemble two long flat rulers, one of which lies on its broad surface, and the other on its edge. By a simple mechanical law, each vibratory motion of the common light is resolved into vibratory motions at right angles to one another.
The polarization of light and heat by refraction is not owing to the chemical composition, but to a want of homogeneity in the molecular structure of the substances through which they pass; for regular crystals and substances which are throughout of the same temperature, density, and structure, are incapable of double refraction. The effect of molecular structure is strikingly exhibited by the circular polarisation in the dimorphic crystals of quartz. In one form the plane of polarization revolves from right to left, and in the other that plane revolves from left to right, although the crystals themselves differ apparently by a very slight and often almost imperceptible variety of forms.
Thus polarization forms the most admirable connection between light, heat, and crystalline structure; showing peculiar arrangements of the molecules in regions otherwise unapproachable, and too refined for our perceptions. Besides, the gorgeously coloured images displayed by depolarization are splendid examples of the power of matter in decomposing light.
The perfect correspondence of the properties of the symmetrical, elastic, and optical axes of crystals with light and heat is another instance of the connection between the latter and crystalline form.
The axis of symmetry is that direction or imaginary line within a crystal, round which all the parts or particles are symmetrically arranged. A medium is said to be elastic which returns to its original form with a resilient force after being relieved from compression, and the axis of elasticity of a crystal is that direction in which it is most elastic. The optic axis is that line or direction through which light passes in one beam according to the law of ordinary refraction. Crystals may have one, two or more optical axes according to their form. Doubly refracting crystals such as Iceland spar have only one principal optic axis in which the whole beam passes according to the ordinary law; in every other direction the beam of light is divided into two polarized rays, one of which called the ordinary ray passes according to the ordinary law, while the other, known as the extraordinary ray, traverses the crystal in a different direction, with more rapidity and according to a different and more complicated law. The velocity of this extraordinary ray is a maximum when at right angles to the principal optical axis, and a minimum when parallel to it.
In perfectly regular crystals like the cube or die, the octohedron, &c., there are three axes of symmetry and of equal elasticity at right angles to one another. In these regular crystals all the axes are optical, so that they have no double refraction.
Right square prisms have two equal rectangular axes of symmetry, two axes of equal elasticity, and one optical axis.
All crystals of the pyramidal and rhomboidal systems have one axis of symmetry, two axes of elasticity, one optical axis; and form coloured circular rings traversed by a black cross when viewed by depolarized light.
Lastly oblique prismatic crystals which have three unequal axes of symmetry have three axes of unequal elasticity, two optical axes; and by depolarization give coloured lamnescata, that is coloured figures having the form of the figure 8 which are traversed by a black cross in two opposite quadrants, and when the crystal is made to revolve, the same figure, but in the complementary colours and traversed by a white cross, appears in the other two quadrants.