Page:VaricakRel1912.djvu/25

 Therefore we can obtain the laws for the reflection of light upon a moving mirror, by replacing u by 2u in formulas (34). However, as the image is located at the object's opposite side of the plane $$X'=0$$, we have to take $$-x'$$ instead of $$x'$$, i.e., we have to subject the light vector to the transformation

Now, it follows from (1)

$$\operatorname{ch}\,2u=\frac{c^{2}+v^{2}}{c^{2}-v^{2}},\ \operatorname{sh}\,2u=\frac{2vc}{c^{2}-v^{2}}$$

and the preceding equations go over to

H. has derived the laws of reflection on a moving mirror on the basis of the presupposition: the image of an object is caused by that space-time transformation (71).

The reflection angle at the moving mirror can be defined in the same way as at a stationary mirror, by means of construction according to the principle of. I only mention the related statements by W. M. and E. , performed by them with respect to the  experiment. From our figure 14 we see, that $$\psi=\Pi\left(u_{1}-2u\right)$$ or $$u_{2}=u_{1}-2u$$, when we denote by $$u_2$$ the perpendicular corresponding to angle &psi;. From this it follows $$e^{-u_{2}}=\left(e^{u}\right)^{2}e^{-u_{1}}$$, or

This is the formula of. However, he assumes v to be positive when the ray moves towards the incident rays. In his formula (1) we have to take v as negative, to bring them into accordance to our definition. In the same way we have to alter his figure.