<p>The angular diameter (in radians) of an <a href="https://en.m.wikipedia.org/wiki/Einstein_ring" rel="noreferrer">Einstein ring</a> is
<span class="math-container">$$\theta = \sqrt{\frac{4GM}{c^2}\;\frac{D_{LS}}{D_S D_L}}\ ,$$</span>
where <span class="math-container">$M$</span> is the lens mass, <span class="math-container">$D_S$</span> and <span class="math-container">$D_L$</span> are the angular diameter distance to the source and lens respectively and <span class="math-container">$D_{LS}$</span> is the angular diameter distance between source and lens.</p>
<p>There isn't therefore any mathematical maximum, it depends on the geometry and lens mass.</p>

CC BY-SA 4.0
2022-03-01T22:58:24.627Z
2022-03-01T22:58:24.627Z
ProfRob
<p>Is there an upper limit to how far out an Einstein ring can be visible? For black holes, is it a fixed multiple of their Schwarzschild radius?</p>

CC BY-SA 4.0
2022-03-01T21:48:40.673Z
What do you mean by "how far out"?
ProfRob
CC BY-SA 4.0
2022-03-01T22:04:37.870Z
@ProfRob Based on the second sentence, one would guess it's angular distance seen by an observer.
uhoh
<black-hole><gravitational-lensing><radius>
What is the maximum radius of an Einstein ring?
2080
# What is the maximum radius of an Einstein ring?

(Asked by: username_0 on 2022-03-01)

Is there an upper limit to how far out an Einstein ring can be visible? For black holes, is it a fixed multiple of their Schwarzschild radius?

**Tags:** black-hole, gravitational-lensing, radius
> **Comments:**
> **username_1**: What do you mean by "how far out"?  
> **username_2**: @ProfRob Based on the second sentence, one would guess it's angular distance seen by an observer.  

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## 1 answers

### Answer by username_1 on 2022-03-01. Score: 5 | Accepted answer

The angular diameter (in radians) of an [Einstein ring](https://en.m.wikipedia.org/wiki/Einstein_ring) is
$$\theta = \sqrt{\frac{4GM}{c^2}\;\frac{D\_{LS}}{D\_S D\_L}}\ ,$$
where $M$ is the lens mass, $D\_S$ and $D\_L$ are the angular diameter distance to the source and lens respectively and $D\_{LS}$ is the angular diameter distance between source and lens.

There isn't therefore any mathematical maximum, it depends on the geometry and lens mass.


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