Fig. 27.
Fig. 28.
A moment's reflection will show that, if what is here stated be correct, on placing a second plate of tourmaline with its axis parallel to the first, the light will pass through both; but that, if the axes be crossed, the light that passes through the one plate will be quenched by the other, a total interception of the light being the consequence. Let us test this conclusion by experiment. The image of a plate of tourmaline (t t, fig. 27) is now before you. I place parallel to it another plate (t' t'): the green of the crystal is a little deepened, nothing more; this agrees with our conclusion. By means of an endless screw, I now turn one of the crystals gradually round, and you observe that as long as the two plates are oblique to each other, a certain portion of light gets through; but that when they are at right angles to each other, the space common to both is a space of darkness (fig. 28). Our conclusion, arrived at prior to experiment, is thus verified.
Let us now return to a single plate; and here let me say that it is on the green light transmitted by the tourmaline that you are to fix your attention. We have to illustrate the two-sidedness of that green light, in contrast to the all-sidedness of ordinary light. The white light surrounding the green image, being ordinary light, is reflected by a plane glass mirror in all directions; the green light, on the contrary, is not so reflected. The image of the tourmaline is now horizontal; reflected upwards, it is still green; reflected sideways, the image is reduced to blackness, because of the incompetency of the green light to be reflected in this direction. Making the plate of tourmaline vertical, and reflecting it as before, it is the light of the upper image that is quenched; the side image now shows the green. This is a result of the greatest significance. If the vibrations of light were longitudinal, like those of sound, you could have no action of this kind; and this very action compels us to assume that the vibrations are transversal. Picture the thing clearly. In the one case the mirror receives, as it were, the impact of the edges of the waves, the green light being then quenched. In the other case the sides of the waves strike the mirror, and the green light is reflected. To render the extinction complete, the light must be received upon the mirror at a special angle. What this angle is we shall learn presently.
The quality of two-sidedness conferred upon light by bi-refracting crystals may also be conferred upon it by ordinary reflection. Malus made this discovery in 1808, while looking through Iceland spar at the light of the sun reflected from the windows of the Luxembourg palace in Paris. I receive upon a plate of window-glass the beam from our lamp; a great portion of the light reflected from the glass is polarized. The vibrations of this reflected beam are executed, for the most part, parallel to the surface of the glass, and when the glass is held so that the beam shall make an angle of 58° with the perpendicular to the glass, the whole of the reflected beam is polarized. It was at this angle that the image of the tourmaline was completely quenched in our former experiment. It is called the polarizing angle.
Sir David Brewster proved the angle of polarization of a medium to be that particular angle at which the refracted and reflected rays inclose a right angle.[17] The polarizing angle augments with the index of refraction. For water it is 52½°; for glass, as already stated, 58°; while for diamond it is 68°.
And now let us try to make substantially the experiment of Malus. The beam from the lamp is received at the proper angle upon a plate of glass and reflected through the spar. Instead of two images, you see but one. So that the light, when polarized, as it now is by reflection, can only get through the spar in one direction, and consequently can produce but one image. Why is this? In the Iceland spar as in the tourmaline, all the vibrations of the ordinary light are reduced to two planes at right angles to each other; but, unlike the tourmaline, both beams are transmitted with equal facility by the spar. The two beams, in short, emergent from the spar, are polarized, their directions of vibration being at right angles to each other. When, therefore, the light is first polarized by reflection, the direction of vibration in the spar which coincides with the direction of vibration of the polarized beam, transmits the beam, and that direction only. Only one image, therefore, is possible under the conditions.
You will now observe that such logic as connects our experiments is simply a transcript of the logic of Nature. On the screen before you are two disks of light produced by the double refraction of Iceland spar. They are, as you know, two images of the aperture through which the light issues from the camera. Placing the tourmaline in front of the aperture, two images of the crystal will also be obtained; but now let us reason out beforehand what is to be expected from this experiment. The light emergent from the tourmaline is polarized. Placing the crystal with its axis horizontal, the vibrations of its transmitted light will be horizontal. Now the spar, as already stated, has two directions of vibration, one of which at the present moment is vertical, the other horizontal. What are we to conclude? That the green light will be transmitted along the latter, which is parallel to the axis of the tourmaline, and not along the former, which is perpendicular to that axis. Hence we may infer that one image of the tourmaline will show the ordinary green light of the crystal, while the other image will be black. Tested by experiment, our reasoning is verified to the letter (fig. 29).
