Page:Elektrische und Optische Erscheinungen (Lorentz) 132.jpg

 we look at two pointsP and Q, which on both sides of the border area, lie in a fixed distance from it, at the intersection of two planes of symmetry.

Let P belong to the space, in which 1 and 2 are overlapping. Similarly, let Q simultaneously lie in 3 and 4. Only values of the light vectors in P and Q shall be given.

§ 99. If the light vector as regards incident motion has the value

$$q\ \cos\left(2\pi\frac{t}{T}+r\right)$$,

it can be represented (for a reflected or transmitted beam that emerges from it) by

$$a\ q\ \cos\left(2\pi\frac{t}{T}+r-b\right)$$,

where a and b are certain constants. In order to mutually distinguish the various cases, we want to append two indices on any of these magnitudes, the first of them is related to the path of the incident light, and the second is related to the beam that arose from it; additionally, also those a and b which remained without prime, are related to the case, when the translation is directed into the side of the incident light, while the primed letters apply to an equal and opposite displacement.

Let in light path 1 be an incident motion (while the system is progressing into the side of the first medium), at which the light vector has the value

$$\cos\ 2\pi\frac{t}{T}$$

From that, in 2 and 4 the light beams emerge which are represented by

$$a_{1.2}\ \cos\left(2\pi\frac{t}{T}-b_{1.2}\right)$$,

and

$$a_{1.4}\ \cos\left(2\pi\frac{t}{T}-b_{1.4}\right)$$,

Afterwards, we imagine this state of motion as reversed. First, we thus assume, that the translation is turned away from