On the action of the second surfaces of transparent plates upon light
M. Arago had conceived that he had proved by an experiment, that at every possible angle of incidence the quantity of light polarized by reflexion was precisely equal to that of the light at the same time polarized by refraction. Dr. Brewster shows in the present paper, that the experiment does not warrant this conclusion; as the phenomena observed from it are the complicated effects of various refractions and reflexions from both surfaces of the glass, each affecting the position of the planes of polarization. By varying the form of the experiment in a way which allowed of the observation of these effects when separate, he is led to the following general law; namely, that a pencil of light reflected from the second surface of a transparent plate, and reaching the eye after two refractions and an intermediate reflexion, contains, at all angles of incidence, from zero to the maximum polarizing angle, a portion of light polarized in the plane of reflexion. Above the polarizing angle, the part of the pencil polarized by reflexion diminishes until the cosine of the sum of the angles of incidence and reflexion equals the cube of the cosine of the difference between these two angles, when it disappears, and the whole pencil has the character of common light. Above this last angle, the pencil contains a quantity of light polarized perpendicularly to the plane of reflexion, which increases to a maximum, and then diminishes to zero, when the angle has attained 90°. The effect of the two refractions in M. Arago’s experiment, was to make the two quantities of light appear equal, when in fact the one was exactly double of the other. The paper concludes with formulae and tables for computing the exact quantities of polarized light at all angles of incidence.