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
, we have to take
instead of
, i.e., we have to subject the light vector to the transformation
(70)
|
|
Now, it follows from (1)
![{\displaystyle \operatorname {ch} \,2u={\frac {c^{2}+v^{2}}{c^{2}-v^{2}}},\ \operatorname {sh} \,2u={\frac {2vc}{c^{2}-v^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff2a3114a47ca8ed0fa97efd029b4840174f19bf)
and the preceding equations go over to
(71)
|
|
H. Bateman[1] 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 Huyghens. I only mention the related statements by W. M. Hicks[2] and E. Kohl[3], performed by them with respect to the Michelson-Morley experiment. From our figure 14 we see, that
or
, when we denote by
the perpendicular corresponding to angle ψ. From this it follows
, or
(72)
|
|
This is the formula of Hicks. 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.[4] In the same way we have to alter his figure.
- ↑ H. Bateman, The reflexion of light at an ideal plane mirror moving with a uniform velocity of translation. Phil. Mag. 18, 892, 1909
- ↑ Phil. Mag. 3, 1902, 15
- ↑ Ann. d. Phys. 28, 1909, 262
- ↑ See also Laue, Das Relativitätsprinzip, 93