Page:Elementary Text-book of Physics (Anthony, 1897).djvu/477

§ 378] $$cbd = 90^\circ,$$ we have $$r + i = 90^\circ$$ also; and since $$\mu = \frac{\sin i}{\sin r},$$ we have $$\mu = \frac{\sin i}{\cos i} = \tan i.$$ Hence the angle of complete polarization is given by the equation $$\tan i = \mu.$$ The fact embodied in this equation was discovered by Brewster, and is known as Brewster's law. The angle of complete polarization is called the polarizing angle. The plane of incidence is the plane of polarization. The vibrations of polarized light are assumed to be at right angles to the plane of polarization. In the transmitted ray is an equal amount of polarized light, the vibrations of which are in the plane of incidence.

If a beam of ordinary light traverse a transparent medium, in which are suspended minute solid particles, the light which is reflected from them is found to be partially polarized. The maximum polarization is found in the light reflected at right angles to the beam. The plane of polarization of the polarized beam is the plane of the original beam and the beam which reaches the eye of the observer.

378. Interference of Polarized Light.—The assumption that has been made in the foregoing descriptions, that the vibrations in the polarized beam are transverse to the direction of propagation, is fully justified, not only by the satisfactory way in which it explains the various modes of production of polarized light and the phenomena connected with it, but also by direct experiment. Fresnel and Arago examined the interference of polarized beams and arrived at the following conclusions: Two rays of light polarized at right angles with each other do not appear to affect each other at all in the same circumstances in which two rays of ordinary light destroy each other by interference. Two rays of light polarized in the same plane act on one another like ordinary light, so that in the two cases the phenomena of interference are absolutely the same. Two rays originally polarized at right angles to each other can afterwards be so modified that they are both polarized in the same plane without acquiring the power of interfering with each other. Two rays polarized at right angles and afterwards brought to the same plane of polarization interfere like ordinary light if they come from the same polarized beam.