446 LIGHT FIG. 15. tion as the planes of reflection become more nearly parallel. The plane in which a polar- ized ray is most easily reflected is called the plane of polarization, and it coincides with the plane of incidence and reflection. The angle of reflection at which polarization becomes most complete with any surface is called the po- larizing angle for that surface, and varies with the substance, according to the following law dis- covered by Brewster: "The polarizing angle of a substance is that angle of incidence for which the reflected polarized ray is at right angles to the refracted ray." Thus, in fig. 15, if s i is the incident, * r the refracted, and if the reflected ray, the polarization is most complete when fi is at right angles to ir. It is still an unsettled question as to whether the vibrations of the polarized ray take place in the plane of polarization or at right angles to it. It is sometimes assumed for convenience of explanation that they take place within it, but it is the opinion of Fres- nel and Cauchy that they are per- pendicular. Mac- Cullagh and Neu- mann regard them as taking place within the plane. Fig. 16 will serve to represent the manner in which the vibrations take place according to Fresnel and Oau- chy, where a c 5, 5 c d is the plane of polar- ization. The majority of physicists are in- clined to regard this as the more probable mode of motion. The following table shows the polarizing angles of a few transparent sub- stances, chiefly according to the observations of Biot and Arago : TABLE OF POLAKIZING ANGLES OF MEDIA.
FIG. 16. SUBSTANCE. Polarizing angle. SUBSTANCE. Polarizing angle. Fluor spar Water 54 40' 52 45 Topaz Iceland spar 5S 40' 58 23 Glass 54 35 Euby 60 16 Obsidian Selenite Amber 56 03 56 28 56 35 Zircon Sulphur Ant glass 63 08 64 10 64 45 Quartz Heavy spar 57 22 58 Chr. lead Diamond 67 42 63 02 When a ray of light from a luminous source falls upon a glass plate at the polarizing an- gle, that portion of it which is refracted is also partially polarized. If that which has passed through one plate is afterward transmitted through several in succession having their sur- faces parallel, the polarization may be made tolerably complete. The planes of polarization of the reflected and the refracted rays are at right angles to each other, as are the planes of polarization of the ordinary and extraordinary rays in Iceland spar. If two plates of tour- FIG. 17. FIG. 18. FIG. 19. maline, a negative uniaxial crystal, which has been cut in sections parallel to its axis, are laid at right angles upon each other, as in fig. 17, the combination will be opaque ; if placed diagonally, as in fig. 18, the opacity will be partial ; and if they are placed parallel to each other, as in fig. 19, the light will pass through both as if they formed one piece. The light in passing through the first plate of tourmaline has been polarized, its vibrations having been reduced to one plane ; or, as it is sometimes explained, all the rays except those which vi- brate in one plane have been sifted out by the crystalline structure of the tourmaline, which has the property when not too thin of destroying the vibrations in the ordinary ray, and allowing only the extra- ordinary ray to pass through. mi Therefore, in order that all the rays which have passed through the first plate may pass through the second, the axes of the two must be parallel. Polarizing Apparatus. There are various pieces of apparatus used in in- vestigating the properties of polarized light, and they al- ways consist of two parts, a polarizer and an analyzer. In the experiment with the re- flecting glass plates, fig. 14, the first plate is the polarizer and the second the analyzer. In the case of the tourmaline plates, figs. 17, 18, and 19, that through which the light first passes is the polarizer, and the other the analyzer ; and in the original experiment with Ice- land spar, the first rhomb was the polarizer and the second the analyzer. Iceland spar, as has been said, is one of the most perfect of polarizing sub- stances, but it does not in its natural form separate the two rays far enough for conve- nience. The desired separation has been ac- complished by a very ingenious device of Ni- col, a London optician, in the construction of a prism which bears his name. A rhombohe-
