# How long is that angle?

sonhouse
Posers and Puzzles 23 Nov '08 18:31
1. sonhouse
Fast and Curious
23 Nov '08 18:31
So this kid is studying gravitational lensing and found out about the famous 1.75 seconds of arc that light bends skimming the surface of the sun that was proven in 1922 by Eddington and Campbell. He found the original equation, Angle=4GM/C^2*R and figured out how far out two beams skimming by the sun would go before they met. He wanted to draw the angle out on paper, his best pen had a 0.25 mm tip and he could lock in the actual angle to draw it out. so starting at one point, the two lines slightly diverging, how long was the line before the two lines actually separated, where a gap finally appears in those quarter millimeter wide lines, and how long do the lines go before they are one millimeter from the top of one line to the bottom of the other?
I would like to see your work, how you approach the math. I know two ways to do it, wondered if anyone would come up with something different. Also, figure out how far out the actual light beams go into space before they cross, the two beams one skimming by on the left side of the sun and the other on the right side. Good luck for all you who take this on!
2. sonhouse
Fast and Curious
24 Nov '08 00:13
I made one mistake, the angle starts out 1 mm wide and goes down to a point, I was putting it in backwards, otherwise the rest is true.