Re post of Light Thought Experiment - This is a re post of the sequel to the question that I posted 3wks ago.?

Question

The scenario is a lighthouse at the North Pole, whose beam rotates at 1 revolution per second. Ignoring attenuation by the earth's atmosphere and the rotation of the earth, my original question was how far along the beam would it be travelling tangentially at the speed of light. The answer that were provided said that the "beam" is not solid and that in fact the photons in the beam are all travelling radially, with no tangential component. This I can accept. Now for my next installment:
Imagine that there is a mirror in the shape of an anulus (ring) at a distance "d" from the lighthouse:
1) What is the value of "d" (let's call it D) such that the intersection of the beam of light and the anulus moves at the speed of light (c)?
2) If the anulus was at a distance of 2D from the lighthouse, what will the speed of the intersection of the beam and the anulus be? Let's call it z.
3) What will I observe as I look towards the anulus from the lighthouse?(i.e. direction of reflected light

The anulus does not move. The intersection between the beam and the anulus is what is moving. The anulus is a continuous circular mirror.

Answer 1

I think I understand your experiment. I'm standing at the anulus observing. I see the light from the lighthouse. Exactly one second later, I see the next flash of light from the lighthouse, no matter the radius of the anulus. To satisfy (1) the perimeter of the anulus must be 186,000 miles, the diameter 186,000 miles / pi or 59,206 miles, and the radius d/2 = 29,603 miles. That's about 7.47 times the earth's radius. For (2), if you double the radius, you double the circumference. Keeping the time the same, that doubles the speed. You already knew that.

For (3), at the lighthouse you see the reflection of the lighthouse beam. To reduce confusion, you could do what real lighthouses or bouys sometimes do: alternating rotations are a different color. But what you would see is the reflection, but delayed by 1/pi seconds, or 318 milliseconds.

I'm guessing at your response. At z=2D, this 'intersection' is travelling at twice the speed of light. There's no physics problem with that. It's not conveying either matter or information faster than the speed of light. You have just contrived two events closer in time to each other than the time light would take to go between them.

Answer 2

If the beam rotates at once per second, it will be rotating at two pi radians per second, and at a distance of 3E8/2pi meters, the beam will be moving with an apparent tangential velocity of the speed of light, and at twice that at twice the distance. Of course, nothing physically moves that fast, and this is no exception. The reflected light will look like the transmitted light two (or four) seconds earlier, and you would see that if you imposed some sort of modulation on the transmitted beam (as by running it through a rotating color filter).

Answer 3

This is a very interesting scenario. However, it does not work in real life. The Reason is that the annulus cannot be made to move at the speed of light.