55.

Suppose now that this wave strikes a reflecting surface, e.g., the surface of an absolute conductor (metal) of infinitely 4 large conductivity. In such a conductor even an infinitely small electric field-strength produces a finite conduction current; hence the electric field-strength $⋿$ in it must be always and everywhere infinitely small. For simplicity we also suppose the conductor to be non-magnetizable, i.e., we assume the magnetic induction $𝖡$ in it to be equal to the magnetic field-strength $𝖧$, just as is the case in a vacuum.

If we place the $x$-axis of a right-handed coordinate system $(xyz)$ along the normal of the surface directed toward the interior of the conductor, the $x$-axis is the normal of incidence. We place the $(x^{\prime }{y}^{\prime })$ plane in the plane of incidence and take this as the plane of the figure ([fig:4]Fig. 4). Moreover, we can also, without

any restriction of generality, place the $y$-axis in the plane of the figure, so that the $z$-axis coincides with the $z^{\prime }$-axis (directed from the figure toward the observer). Let the common origin $O$ of the two coordinate systems lie in the surface. If finally $\theta$ represents the angle of incidence, the coordinates with and without accent are related to each other by the following equations:

$$\begin{gathered} x\&=x^{\prime }\cos \theta -y^{\prime }\sin \theta \&x^{\prime }\&=\phantom{-}x\cos \theta +y\sin \theta \\ y\&=x^{\prime }\sin \theta +y^{\prime }\cos \theta \&y^{\prime }\&=-x\sin \theta +y\cos \theta \\ z\&=z^{\prime }\&z^{\prime }\&=z. \end{gathered}$$

By the same transformation we may pass from the components of the electric or magnetic field-strength in the first coordinate system to their components in the second system. Performing this transformation the following values are obtained from [eqn:(54)] (54) for the components of the electric and magnetic field-strengths of the incident wave in the coordinate system without accent, $\mathsf{E}{x} &= -\sin\theta · f \qquad & \mathsf{H}} &= \phantom{-}\sin\theta · g \ \mathsf{E{y} &= \phantom{-}\cos\theta · f & \mathsf{H}} &= -\cos\theta · g \ \mathsf{E{z} &= g & \mathsf{H} &= f.

\Label[eqn]{(55)}\tag*{\upshape (55)}$ Herein the argument of the functions $f$ and $g$ is $t-\frac{x^{\prime }}{c}=t-\frac{x\cos \theta +y\sin \theta }{c}.\mathrm{\backslash Label}[eqn](56)\text{upshape (56)}$