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View Full Version : Light paths, and self magnification.

WaxRubiks
2012-Feb-19, 02:28 PM
16309

This is a question about light paths.
If light were emitted from a large gravitational object, at point A, and its path is curved by the warpage of space-time, when it gets to point B, if it could look back at where it came from, would it see that point as point C(ie at a tangent to the path)?

I know light isn't like a space ship, but I wondered whether the reality, for the light, of where it came from, and the new shape of the object it was emitted from would affect the way its path would curve. Less curvature, more, or no difference? Or less or more(or the same) "pull", from the object as it flattens?

I suppose that the apparent shape of the object it was emitted from would be more of a squashed ball, which is my secondary question. What shape would an object appear to hold, under self magnification?

Hornblower
2012-Feb-19, 05:45 PM
16309

This is a question about light paths.
If light were emitted from a large gravitational object, at point A, and its path is curved by the warpage of space-time, when it gets to point B, if it could look back at where it came from, would it see that point as point C(ie at a tangent to the path)?

Yes, as I understand it.

I know light isn't like a space ship, but I wondered whether the reality, for the light, of where it came from, and the new shape of the object it was emitted from would affect the way its path would curve. Less curvature, more, or no difference? Or less or more(or the same) "pull", from the object as it flattens?

I don't know what you mean by "new shape." The ball is the same shape after the light is well on its way as it was at the moment the light was emitted.

I suppose that the apparent shape of the object it was emitted from would be more of a squashed ball, which is my secondary question. What shape would an object appear to hold, under self magnification?I would expect the ball to look round, but larger than one of the same radius but negligible mass.

WaxRubiks
2012-Feb-20, 08:05 AM
I don't know what you mean by "new shape." The ball is the same shape after the light is well on its way as it was at the moment the light was emitted.

I mean the shape it would appear to anyone at B, if you could see the other side of the object, as if it were made of glass.

I wondered, as you can see slightly behind the object, and it appears bigger, whether the object would appear to be a flattened ball.

You would have to plot the light path from lots of points on the surface, including from behind(hypothetical paths through the object) to see if it would still appear as just a large sphere, or a flattened sphere, or anything else.

pzkpfw
2012-Feb-20, 10:01 AM

WaxRubiks
2012-Feb-20, 10:35 AM
yes, I know I've asked similar questions before, but these are new.

1. How does the apparent size and shape of the large object affect the path of the light at different parts of its path?

2. What is the apparent shape of the large object at different distances away from the large object?

Kuroneko
2012-Feb-20, 02:03 PM
For weak gravitational lensing in a static gravitational potential Φ, pretend space is a material with refractive index n = 1-2Φ/cē, and solve the corresponding optics problem.

WaxRubiks
2012-Feb-20, 03:27 PM
I was thinking of strong gravitational fields.

grapes
2012-Feb-20, 08:24 PM
Look at the line between B and the center of the sphere. Wouldn't your diagram be symmetrical about that line? Even rotationally symmetric?

WaxRubiks
2012-Feb-21, 04:05 AM
Look at the line between B and the center of the sphere. Wouldn't your diagram be symmetrical about that line? Even rotationally symmetric?

yes, the large object would look round, but I am wondering about depth. Would it be possible to work out the whole shape of the object theoretically, by working out light paths(to B) from all over the surface of the object?
And as I said, maybe you could work out hypothetical paths of points on the surface behind the object, that went through the object, to find out what the hidden surface looked like. I don't know whether the paths through the object would include the refractive index of that object, or not, or maybe just the null path.....

ETA: I guess you wouldn't include the refractive index of the object.

WaxRubiks
2012-Feb-22, 05:28 AM
16322

My guess is that the large object would look like the squashed dotted circle(ball), but that's just a guess.

grapes
2012-Feb-22, 03:12 PM
16322

My guess is that the large object would look like the squashed dotted circle(ball), but that's just a guess.In your diagram, notice the point where the dotted ellipse and the sphere intersect. What happens there?

WaxRubiks
2012-Feb-22, 04:00 PM
In your diagram, notice the point where the dotted ellipse and the sphere intersect. What happens there?

well it's only a guess diagram, but nothing happens there, does it?

The sphere would be magnified out, and a part of the sphere closer to B would be magnified out to that point of intersection.

ngc3314
2012-Feb-22, 05:18 PM
There was a nice video (http://apod.nasa.gov/htmltest/rjn_bht.html) by APOD co-originator Robert Nemiroff which shows how gravitational lensing acts near a neutron star, by imagining that outlines of the terrestrial continents painted on its surface. It always looks round, but that pattern shows that we see its surface distorted from the low-gravity appearance, and from close up we see the same point of the surface multiple times.

WaxRubiks
2012-Feb-22, 08:49 PM
http://www.bautforum.com/attachment.php?attachmentid=16337&d=133015098016337

http://www.bautforum.com/attachment.php?attachmentid=16338&d=133015271216338

probably very unscientific, but I wrote a computer program to plot light paths in a sort of Newtonian way, and I got this diagram, with X being the observer, Z being the gravitational body, and Y being the observed magnified version of Z.

It should be done with a relativistic model, but I thought it was interesting, well the best I could do, anyway.

It was sort of what I imagined any way, with the flatter rear.