By Ludwik Silberstein

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**Extra resources for Elements of the Electromagnetic Theory of Light**

**Sample text**

V lt vJ V-^2 vz c/ = ns = 0, \ = t -4 cl < ' (35) -t " \/^3 are tne 80 If the normal is called principal velocities of propagation. the the electrical waves are axis, propagated with along first the second or the third principal velocity (according to the direction of D), and so on, by cyclic permutation. In order to determine the directions s', s" in which D must ELECTEICAL AXES 42 vibrate in each of the above three cases split, the if wave is not to return * to the equation D=E cI already obtained from - (En)n, This gives, for (5), p.

E. if they are not to split into two trains of waves, then the vector must have one of the two directions D or 8 DIRECTION OF VIBRATIONS 38 where the + signs, being, of course, irrelevant, have been omitted. These two privileged directions s' and s" of light oscillations, belonging to a given normal n, are perpendicular to one another. In fact, denoting the vector operator in (26) by w, we can write Fresnel's equation no>n = 0, s" = . . (266) and, instead of (27), s' = a/n, to"n, and since

Note on the Transition Layer. Reflection 5. e. to the axis of z, while the of the boundary magnetic contained in the plane of incidence. In the habitual terminology, the incident light is polarized in the plane of vector is polarization. e. writing down the boundary conwhich now require the continuity of the whole electric force and of the whole magnetic force, we get again a x = a, sin a sin p = n, and for the ratios of the electric amplitudes, Proceeding as before, ditions : EI K E sin (a - sin (a + ~ E 2 cos a sin ' sin (a ft) p + P These formulae are again identical with those known as Fresnel's formulae for incident light polarised in the plane of The electric force again corresponds to Fresnel's incidence.

### Elements of the Electromagnetic Theory of Light by Ludwik Silberstein

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