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I was reading about gravitational lensing. I was just curious to know if there are any formulae or methods to find the angle at which the light deflects due to strong gravitational lensing?

And how far should that massive object be present so that we can observe multiple images of the observing object?

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    $\begingroup$ Hi Ishan, it's a great question, but on this site you're expected to have done a little research yourself before asking, i.e. at least read the wiki, have a look at related SE questions (e.g. here, here, and here), and maybe have a look at the first few Google hits, like this and this. I suggest you take a look at those links and come back with more specific questions to things you don't understand :) $\endgroup$
    – pela
    Commented Sep 12, 2019 at 6:50
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    $\begingroup$ @Pela (and upvoters) None of those links provide anything like a quantitative answer to this question. $\endgroup$
    – ProfRob
    Commented Sep 18, 2019 at 18:45
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    $\begingroup$ @RobJeffries Yeah, you're right. The question was a bit different when I wrote this comment, and seemed to me like the OP simply wanted more general knowledge on strong lensing. $\endgroup$
    – pela
    Commented Sep 18, 2019 at 20:20

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Absolutely: $$\theta = \frac{4GM}{c^2b},$$ where $\theta$ is the angle of bending, $G$ is the gravitational constant, $M$ is the mass of the star/blackhole/whatever, $c$ is the speed of light, and $b$ is the "impact parameter", the distance from the light ray to the center of the mass on its closest approach if it was NOT deflected (i.e., $b=0$ for an impact).

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    $\begingroup$ This is the weak field approximation. The question was asking about strong lensing. $\endgroup$
    – TimRias
    Commented Sep 18, 2019 at 13:34
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    $\begingroup$ This is a weak lensing formula that doesn't address the question asked. $\endgroup$
    – ProfRob
    Commented Sep 18, 2019 at 18:46
  • $\begingroup$ I do not recall the bold term being there when I answered it! $\endgroup$
    – Maury Markowitz
    Commented Sep 19, 2019 at 13:45
  • $\begingroup$ @MauryMarkowitz that's right, I put it in boldface because apparently you didn't see it. $\endgroup$
    – ProfRob
    Commented Apr 5, 2021 at 11:00

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