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- Thread starter AUK 1138
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The easiest way to think about it is if you have a solid rod held by an observer alongside it, moving at the same speed.

The observer won't notice anything relativistic, because from their point of view nothing is moving at relativistic speeds (except the surroundings, which, for this thought experiment are just empty space).

So if the observer sees a focused spot of light from the lens near the end of the rod, so will anyone else who can see the rod (because we must keep causality).

Which means that the focal length of the lens just follows http://en.wikipedia.org/wiki/Length_contraction" [Broken] like the rod does, assuming that you have an inertial (constant velocity) frame of reference. So you just divide the length by gamma.

regards, Michael

The observer won't notice anything relativistic, because from their point of view nothing is moving at relativistic speeds (except the surroundings, which, for this thought experiment are just empty space).

So if the observer sees a focused spot of light from the lens near the end of the rod, so will anyone else who can see the rod (because we must keep causality).

Which means that the focal length of the lens just follows http://en.wikipedia.org/wiki/Length_contraction" [Broken] like the rod does, assuming that you have an inertial (constant velocity) frame of reference. So you just divide the length by gamma.

regards, Michael

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This sounds to me like an argument that the index of refraction of the material is not invariant, as the point where the lightray's converge should be invariant.

In fact, the index of refraction of empty space being increased by a gravitational field is one explaination of the fact that relative to an outside observer the speed of light varies as one decends into a gravitational well (always locally c, but dime dilated relative to the outside observer.)

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