Page:Optics.djvu/204

 in which the refracting power is supposed to be respectively greater than unity, equal to that number, and less than it.

This law applies equally well to substances which, like the diamond and sulphur, never produce more than an incomplete polarization, for the quantity of light reflected is invariably a minimum for the angle so determined.

If the mode of observation which we have applied to smooth glass plates be universally employed, it may serve to show that polarization when complete is always a modification exactly of the same kind, for all substances: for when a beam of light has been once polarized, it will equally pass through all substances, with the exception mentioned above, provided each be presented to it under its proper angle, and whatever be the nature of the first or second substance employed, the variation of intensity in the light after the second reflexion is always subject to the same laws.

To represent these circumstances geometrically, let us consider a ray $$II'$$ (Fig .) polarized by reflexion on a glass plate $$LL$$, and through any one of the molecules composing it, let there be drawn three rectangular axes $$cz, cx, cy$$, the first coinciding with the ray, the second in the plane of reflexion $$SIC$$, the third perpendicular to both the others. Then when the ray $$II'$$ meets a second glass $$L'L'$$ placed so as to produce no reflexion, the reflecting forces which emanate perpendicularly from the glass, must be perpendicular to the axis $$cx$$; moreover they must act equally on molecules lying towards $$cx$$, and towards $$cx'$$, for if the glass be turned a little from the position of no reflexion, the effects are found to be symmetrical on all sides of that position. The action, therefore, of these reflecting forces, in this position, cannot make the axis $$xcx'$$ turn either to the right or left, any more than the force of gravity can turn a horizontal lever with equal arms. They cannot bring the axis into their own plane, in which we see it was in the first reflexion, by which the polarization took place on the glass $$LL$$. This proves that it is on that axis that the properties of the luminous molecules depend. We will for that reason call it the axis of polarization, and suppose its direction similarly and invariably determined for each molecule. Farther, for the sake of conciseness, we will call $$cz$$ the axis of translation; but we do not suppose this

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