Page:Scientific Memoirs, Vol. 1 (1837).djvu/87



HEN two systems of waves, of equal intensity, propagated in the same direction, and polarized perpendicularly to each other, differ in their path by an odd number of quarter-undulations, the particles in the resulting system of waves will describe small circles of a similar velocity around their points of equilibrium; that is to say, the light will be circularly polarized. Every means of equally satisfying these two conditions, namely, that of the similar intensity of the system of waves polarized perpendicularly to each other, and that of the determinate difference of path, consisting of an uneven number of quarter-undulations, will therefore furnish a method of circularly polarizing light. Fresnel and Airy have effected this in different ways. The third mode, which I shall here explain, is in practice at least as convenient as those hitherto used, and gives moreover a fuller explanation of the phænomena of compressed and cooled glasses in polarized light.

The condition of the equal intensity of the systems polarized perpendicularly to one another is satisfied by Fresnel by polarizing the incident light in a plane which forms an angle of 45° or 135° with the plane of the total reflexion in a glass parallelopiped. The quantities of light polarized in, and also perpendicularly to the plane of reflexion, are then, according to Fresnel's formula of intensity, equal to each other. He obtains the difference of phases of a quarter-undulation by twice-repeated total reflexion, since after a single one under the given circumstances the periods of vibration of the reflected waves no longer coincide, but exhibit a difference of phases of an $1/undefined$-undulation.

The method which Airy has adopted depends upon another principle. When a thin plate of an uniaxal crystal cut parallel to the axis, and whose axis forms with the plane of polarization of the incident light an angle $$a$$, is observed through a rhombohedron of Iceland spar, the principal section of which is inclined toward the plane of primitive of polarization under the angle $$b$$, then, if $$I_o$$, $$I_e$$ indicate the intensities