07 Apr 16
Originally posted by sonhouseIndeed this will somewhat reduce the relative intensity around 1µm. Do the math and you can find out exactly how much.
For what it is worth, the surface temp of Sirius is about 10,000K. That would put the peak closer to the blue end of the spectrum. Sirius IS a blue star.
08 Apr 16
Originally posted by twhiteheadIt is interesting, according to that article, about one paragraph devoted to solar lenses, Einstein already knew what I figured out, the focus starts at about 500 AU and continues. Do don't know if he figured the focus eventually stops or not, I figured that one out on my own.
Using the sun as a sort of telescope has been proposed:
https://en.wikipedia.org/wiki/Gravitational_lens#Solar_gravitational_lens
Using gravitational lensing to find free floating planets is also a thing:
https://en.wikipedia.org/wiki/Gravitational_microlensing#Detection_of_extrasolar_planets
Lensing due to a free floating planet is quite signific ...[text shortened]... ldn't find a source, but I believe the star momentarily gets several times brighter than normal.
08 Apr 16
Originally posted by sonhouseThe focus does not stop.
It is interesting, according to that article, about one paragraph devoted to solar lenses, Einstein already knew what I figured out, the focus starts at about 500 AU and continues. Do don't know if he figured the focus eventually stops or not, I figured that one out on my own.
16 Apr 16
Originally posted by twhiteheadI 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.
The focus does not stop.
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.
17 Apr 16
1 edit
Try as I might I cannot follow your explanation. It remains wrong. The focus is actually continuous from the centre of the sun off to infinity. The only reason why there is a minimum in practice is the suns shadow. There is no maximum.
A black hole of the same mass as the sun would have a much shorter minimum.
To create an equivalent lens out of glass you would have a point in the centre with concave sides going down to flat. I couldn't find a suitable image on the internet.
17 Apr 16
Originally posted by twhiteheadDo you agree the wavefront of light from any star is mostly spherical?
Try as I might I cannot follow your explanation. It remains wrong. The focus is actually continuous from the centre of the sun off to infinity. The only reason why there is a minimum in practice is the suns shadow. There is no maximum.
A black hole of the same mass as the sun would have a much shorter minimum.
To create an equivalent lens out of gla ...[text shortened]... centre with concave sides going down to flat. I couldn't find a suitable image on the internet.
And do you agree the deflection angle goes down the further you get from a center of mass?
17 Apr 16
Originally posted by twhiteheadIt is therefore impossible for the focus line to go forever. As the wavefront from a star goes away from the center line connecting the two stars, at some point the divergent line of light will be at an angle that just equals the angle of deflection of the sun. At that point the further line of sight travel for that photon is parallel to the line drawn between the center of mass of the two stars.
Yes.
And I believe we have discussed this before.
What is difficult about seeing that? That would be by definition, the end of the focus.
The other angles of light will do their focus thing only at individual points and then the light at that point starts diverging again like a normal lens FOR THAT ONE POINT IN SPACE. The effective focal length changes for light passing the sun further and further away from it's center of mass, getting longer and longer till like I said, the angle of light in the distance star's wavefront can only be bent into a line parallel with the line drawn between the center of mass of the two stars.
It is pretty simple. You don't need to be an Einstein to see the path light takes once he has done the heavy lifting.
17 Apr 16
Originally posted by sonhouseNo, it isn't.
It is therefore impossible for the focus line to go forever.
As the wavefront from a star goes away from the center line connecting the two stars, at some point the divergent line of light will be at an angle that just equals the angle of deflection of the sun.
And just before that, it reaches the focal point at infinity.
What is difficult about seeing that?
I can see that. It doesn't prove your case.
That would be by definition, the end of the focus.
Agreed. Still, the focal line goes to infinity just before the light gets to an exact parallel.
The other angles of light will do their focus thing only at individual points and then the light at that point starts diverging again like a normal lens FOR THAT ONE POINT IN SPACE. The effective focal length changes for light passing the sun further and further away from it's center of mass, getting longer and longer till like I said, the angle of light in the distance star's wavefront can only be bent into a line parallel with the line drawn between the center of mass of the two stars.
Which happens when the focal point gets to infinity.
It is pretty simple.
Yes it is. Yet you still got it wrong.
17 Apr 16
Originally posted by sonhouseJust to be clear, what you are claiming is that light from Sirius is focused by the sun. Imagine the light from Sirius as being composed of a set of hollow cones all fitting into each other. The light travelling directly, so the angle of the apex of the cone is zero, is focused to the focal length of the sun if one considers it as a lens. Light which is diverging slightly as it approaches the sun, in other words the angle of the apex of the cone is greater than zero, will be focused to a point further along so there is a line. What you seem to be saying is that the light in wider cones is deflected by a smaller angle due to the inverse square law (it gets less close to the sun) so the line must terminate somewhere. As an idealisation I don't think that this is right, although in practise it probably is due to losses from dust and so forth. The amount of light reaching the line will decrease but you should get some light focused to any point along it. What is true is that some light coming from Sirius will not be focused to a point. If the angle at the apex of the cone is below some critical angle it will be focused to the line. If it is above this critical angle then it will still be diverging when it's gone past the sun. At the critical angle it's focused to the point at infinity.
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 cen ...[text shortened]... ps focusing about 1.5 light years out. Also much less light focused but it does of course focus.
17 Apr 16
IOriginally posted by DeepThoughtThere is a point at which light will cease to be focused from a given source, like Sirius. You know light diverges from Sirius since it is a spherical wavefront and only that light that grazes past the surface of the sun will be focused at the full 1.75 arc seconds of deflection. Even that light is going to be deflected slightly less than 1.75 seconds of arc because of the angle the light hits the surface of the sun. VERY slightly.
Just to be clear, what you are claiming is that light from Sirius is focused by the sun. Imagine the light from Sirius as being composed of a set of hollow cones all fitting into each other. The light travelling directly, so the angle of the apex of the cone is zero, is focused to the focal length of the sun if one considers it as a lens. Light which ...[text shortened]... rging when it's gone past the sun. At the critical angle it's focused to the point at infinity.
But as the light from Sirius enters the solar system from angles much greater than that grazing the surface, there is more of it geometrically speaking, a bigger area around a circle higher above the surface of the Sun. Eventually you get to a point where the angle of divergence of light from Sirius equals the convergence of light going past the sun and at that point the only thing the light will do is forever now travel in a line parallel to the line I drew from the center of Sirius through the center of the sun.
The inner limit is about 80 billion Km, first focus, to a line of focus going out about 8 light years and for stars with similar diameters, the line of focus will extend to about the distance of the separation of the two stars.
Don't know what is so hard to see about that.
Also, it is not inverse square, the radius part of the formula is linear, first power, not squared so the change of convergence angle is much more gentle than the inverse square law of the force of gravity or the intensity of light from a spherical wavefront.
The formula is D (divergence angle in radians) = 4GM/C^2 r. Mass in Kg, r in meters, C^2 Speed of light squared. Notice the r is not squared so the convergence angle is just a linear function, 1 r= 1.75 arc seconds, 2r, 0.83 arc second, 4 r= 0.4ish arc second, 8 r= 0.2 ish arc seconds and so forth.
17 Apr 16
1 edit
Originally posted by sonhouseYour first two paragraphs are identical to what I was saying, apart from the first sentence. Consider the limiting case, that is to say the case where light from Sirius is left "forever now travel[ling] in a line parallel to the line I drew from the centre of Sirius though the centre of the sun." This is what I mean by focused on the point at infinity, I'm calling the angle at the apex of this cone (at Sirius) the critical angle. If you take the angle at the apex of the cone, which I'll call theta, of the light focused on the point at your 8 light year limit it must be less than this critical angle. Choose some angle between the critical angle and theta. The light cannot be moving parallel to your line as the angle of this cone of light is less than the critical angle, what is more it must be converging to a point. Since the angle is also greater than theta it must be focused at a point further away from the sun than your 8 light year limit. This follows from continuity.
There is a point at which light will cease to be focused from a given source, like Sirius. You know light diverges from Sirius since it is a spherical wavefront and only that light that grazes past the surface of the sun will be focused at the full 1.75 arc seconds of deflection. Even that light is going to be deflected slightly less than 1.75 seconds of ar ...[text shortened]... arc seconds, 2r, 0.83 arc second, 4 r= 0.4ish arc second, 8 r= 0.2 ish arc seconds and so forth.
17 Apr 16
Originally posted by sonhouseIts where do you get the 8 light years from that I have a problem. Where did that figure come from?
The inner limit is about 80 billion Km, first focus, to a line of focus going out about 8 light years and for stars with similar diameters, the line of focus will extend to about the distance of the separation of the two stars.
Don't know what is so hard to see about that.
I feel the same way. It seems to me to be obvious that there has to be continuity from maximum deflection all the way to parallel lines and eventually to virtually no deflection. This has to include the point at infinity which is essentially identical to the parallel lines, and everything in between. The only reason the inner limit exists is because the suns shadow blocks any light that would have focused closer. There is no logical reason for an outer limit.
17 Apr 16
2 edits
Originally posted by twhiteheadNo, the inner limit is not due to the shadow of this sun. Imagine building a gigantic glass lens where the profile of the lens is chosen to exactly mimic the gravitational effect of the sun on light passing through it. In this case there is no possibility of a shadow effect. Parallel rays of light impinging on a lens are focused to the point at the focal length of the lens.
Its where do you get the 8 light years from that I have a problem. Where did that figure come from?
[b]Don't know what is so hard to see about that.
I feel the same way. It seems to me to be obvious that there has to be continuity from maximum deflection all the way to parallel lines and eventually to virtually no deflection. This has to include t ...[text shortened]... blocks any light that would have focused closer. There is no logical reason for an outer limit.[/b]
I'm not sure about this any more, so I'll restate my argument as my previous post wasn't clear, ideally we'd have a diagram. Let the angle between the light as it is emitted from Sirius and the line drawn between Sirius and the centre of the lens be theta. For the light rays for which theta is zero the point of focus is the focal length of the lens. This is sonhouse's inner limit. In "real life" the focus will be a small distance out from that due to your shadow effect, but the inner limit is not due to the shadow, it is intrinsic to the set up. You'd need the incoming light to be already converging (before being influenced by the lens) for it to reach a point of focus closer than the focal point. As theta increases to the critical value, when the rays are left travelling parallel to the imaginary line joining Sirius and our lens, in other words the light is focussed on the point at infinity, by continuity the point of focus must pass through each point between the focal point and the point at infinity.
The 8 light year figure is the distance of the sun from Sirius. However, I'm not convinced sonhouse is wrong any more. For its light to be focused to the point at infinity the source has to be at the focal length of the lens (which is 8.0E7 clicks from the sun). I'm not sure what happens any more.