Elements of the Electromagnetic Theory of Light

Cover Elements of the Electromagnetic Theory of Light
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In the direction of the negative 7/-axis.
Let us now see what the properties of the reflected waves are, after the "limiting angle" a = w = arc sin n has been exceeded.
Take, for example, the case in which the incident light is rectilinearly polarized under the angle = 45 relatively to the plane of incidence. Let P be the component of E in the plane of incidence, and Z its component along the -axis. Let Pj, Z l have similar meanings for the reflected wave. Thus P l and Z l will be what has been
... denoted by E l in (15) TOTAL EEFLECTION 33 and in (18) respectively, and since (for = 45) P = Z, we shall have PI _ _ tan (a - ft) sin (a + ft) = _ cos (a + P) ^ tan (a + 0) ' sin (a - ft) ~ cos (a - ft)' Since sin ft > 1, this ratio will have a complex value, say pe iA where p and A are real. The former will be the ratio of the absolute values [PJ, \Z^\ or the ratio of the amplitudes, and the latter the phase difference of the component con- tained in the plane of incidence and the component normal to this plane.

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