FYKOS Year 30 Series 4 Problem 5 — weird atmosphere · FYKOS 30 #30.4.5
Physics · optics
Problem
Have you ever seen such a weird atmosphere? Up to a certain height the speed of light inside it is constant, v0, but from that certain height the speed of light starts increasing linearly as v(Δh)=v0+kΔh. At one point, exactly at the height where the speed of light starts changing, light beams are sent upward in all directions. Show that all these beams move along circular arcs and determine the radii of these arcs. Also find out the distance between the place where the the light was emitted and the point where the beams return to the original height.