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Been thinking about the first part. In 1 second the light rays are going to be 300,000km apart. Your unlikely to be able to create an experiment where the two rays have enough time and distance to catch up to each other.
I've done some quick calculations and I make it about half an hour. Fair amount of guess work and assumptions in there mind. In this time light can travel about four times the distance from the Earth to the Sun. (~4AU).
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