Originally posted by twhitehead
The focus does not stop.
I deg to biffer with you. Look at the two competing effects: One is the deflection angle which is a variable, getting weaker linearly as you go away from the center of mass.
Then there is the starlight. Any starlight. So you have a star, one I used as a model: Sirius, about 8 light years away.
If you draw a line between the center of Sirius to the center of our sun, then realizing the wavefront from Sirius or any other star is essentially spherical so you see for light flying out at 90 degrees from that centerline (plotting two dimensionally right now) that light has zero chance of being focused I think you have to admit.
So we see angles of that light front that is not 90 degrees, but say 1/10th of a degree, 6 minutes. By the time this light gets to the sun it is striking out at an angle that, when it intercepts a line you might make going from the center of the sun at right angles to the line from center to center of the stars, the height above the sun's surface would invoke a deflection angle way smaller than that 6 minutes of arc that particular light path takes.
There would be some tiny deflection but not near enough to focus.
Those two competing effects is what limits the length of the focal line.
So analyze angles less than that 6 minutes, and instead go 6 SECONDS of arc. Sirius is about 2.6 parsecs away so one arc second would be 2.6 AU in distance. 6 seconds of arc from Sirius to the sun would be a distance above the sun of about 15 AU or in other words, light at 6 seconds off from the center line would pass by the sun about 25 billion Km. Now remember, the angle of deflection very close to the Sun's surface is only 1.75 odd seconds of arc.
At 25 billion km up from the suns surface the deflection angle would be about 1/35,000 of that 1.75 arc seconds or about 5/100,000 of an arc second.
If you chase down smaller and smaller angles like that you find an angle at which the deflection can only straighten the light path out making it go parallel to the line drawn between center of Sirius and center of sun. That is the end of focus and it turns out the focus stops at around the same distance between Sirius and the sun, on the opposite side of the sun of course and that distance is about also 8 light years. The same for Alpha Centauri, about 4 light year focus.
I did it for Jupiter and it turns out the size matters also so the light from Sirius passing by near Jupiter stops focusing about 1.5 light years out. Also much less light focused but it does of course focus.