FYKOS Year 36 Series 6 Problem 4 — light faster than light · FYKOS 36 #36.6.4
Physics · mechanics · optics
Problem
There is a laser in the distance from a large screen. Initially, the laser shines on the screen so that the distance from a laser spot on the screen to the laser is . Then at the time , we begin to rotate the laser at a uniform angular speed . Consequently, the distance of the spot on the screen from the laser decreases to and then increases back to . What is the speed of this laser spot relative to the screen? Is it possible that the spot moves at a speed greater than the speed of light in a vacuum? Is there a limit, can it be infinite? How (qualitatively) does this speed depend on the spot's position on the screen? The whole apparatus is in a vacuum.Intuitive explanation
This problem explores how a rotating laser beam's spot can move along a distant screen faster than the beam itself travels—a classic example of how apparent motion can exceed without violating relativity. The key insight is that the spot's speed depends on the geometry: as the beam angle changes, the perpendicular distance to the screen changes rapidly, and small angular changes translate into large lateral displacements when the screen is far away. Think of it like a searchlight beam sweeping across a distant cloud—the spot can race across at any speed depending on the beam's angle and the screen's distance. The speed diverges to infinity when the beam grazes the screen (nearly parallel to it), which is physically allowed because no information or energy travels faster than along the screen itself.
Intuitive explanation
This problem explores how a rotating laser beam's spot can move along a distant screen faster than the beam itself travels—a classic example of how apparent motion can exceed without violating relativity. The key insight is that the spot's speed depends on the geometry: as the beam angle changes, the perpendicular distance to the screen changes rapidly, and small angular changes translate into large lateral displacements when the screen is far away. Think of it like a searchlight beam sweeping across a distant cloud—the spot can race across at any speed depending on the beam's angle and the screen's distance. The speed diverges to infinity when the beam grazes the screen (nearly parallel to it), which is physically allowed because no information or energy travels faster than along the screen itself.