<p>The expression <span class="math-container">$1.22 \frac\lambda D$</span> (in radians) represents the distance between the center of an Airy disk and the first minimum of an Airy disk that results from a perfect lens with a perfectly circular aperture and a perfectly focused point source. That assumes a bit too much perfection for some, who also see using the center of the first minimum as a bit generous. In those people's minds, it is best to reduce the factor of 1.22 to (approximately) one, resulting in <span class="math-container">$\frac\lambda D$</span> as the angular resolution.</p>
<p>Regarding the factor of <span class="math-container">$2.06\times10^5$</span> arc seconds, that is one radian.</p>

CC BY-SA 4.0
2020-09-20T18:02:21.533Z
2020-09-20T18:02:21.533Z
David Hammen
<p><span class="math-container">$2.06 \times 10^5$</span> is the <a href="https://www.google.com/search?q=radian+arcsecond+conversion&amp;oq=radian+arcs&amp;aqs=chrome.3.69i57j0l7.12068j0j7&amp;client=ubuntu&amp;sourceid=chrome&amp;ie=UTF-8" rel="nofollow noreferrer">radian arcsecond conversion</a>, equal to <span class="math-container">$180 \times 60 \times 60 / \pi$</span> .</p>
<p>The <span class="math-container">$1.22$</span> is a geometrical factor applicable to circular apertures, as outlined in <a href="https://en.wikipedia.org/wiki/Angular_resolution#The_Rayleigh_criterion" rel="nofollow noreferrer">Wikipedia</a>.</p>

CC BY-SA 4.0
2020-09-20T01:23:08.203Z
2020-09-20T16:15:52.523Z
2020-09-20T16:15:52.523Z
Keith McClary
<p>I have recently learned about angular resolution and its dependence on the ratio λ/D. There seem to be three different equations for angular resolution that I have come across. One of these has the number 1.22 (radians), while the other contains the number 206,000 (arcseconds). A third equation states that angular resolution can be found just with the ratio λ/D. I have attached a picture of these three different equations - please pardon the bad merging!</p>
<p>Naturally, this has caused some confusion on what situations each of these equations apply to. Would one of these be more relevant to an interferometer — while another is for a single telescope? I'd like to share that these equations come from the textbooks &quot;Foundations of Astrophysics&quot; (Ryden &amp; Peterson) and &quot;Understanding Our Universe&quot; (Palen, Kay &amp; Blumenthal). If anyone has come across these equations, I'd be grateful for some advice on how to distinguish them (i.e. what situations or conditions they apply to).</p>
<blockquote>
<p><span class="math-container">$$\theta_\text{min}[\text{rad}] = 1.22 \frac{\lambda}{D}$$</span>
<span class="math-container">$$\theta = 2.06 \times 10^5 \frac{\lambda}{D}~\text{arcseconds}$$</span></p>
<p>A telescope's resolution is determined by the ratio <span class="math-container">$\lambda/D$</span>.</p>
</blockquote>

CC BY-SA 4.0
2020-09-20T03:07:58.587Z
Welcome to Stack Exchange! I've kept a link to the screen shot but written out the equation as a block quote using [MathJax](https://math.meta.stackexchange.com/q/5020/284619). Screen shots of text or equations are discouraged whenever the information can be written out explicitly. It helps in several ways; some people use screen text readers or other software, it can be easily copied and reused, and it can then be found using site searches.
uhoh
CC BY-SA 4.0
2020-09-20T14:28:56.210Z
@MikeG thanks for the fixer-upper. I attribute these glitches to "cosmic rays"
uhoh
<astrophysics><angular-resolution><interferometry>
What is the difference between these various Angular Resolution formulas?
Adrian S.
# What is the difference between these various Angular Resolution formulas?

(Asked by: username_0 on 2020-09-19)

I have recently learned about angular resolution and its dependence on the ratio λ/D. There seem to be three different equations for angular resolution that I have come across. One of these has the number 1.22 (radians), while the other contains the number 206,000 (arcseconds). A third equation states that angular resolution can be found just with the ratio λ/D. I have attached a picture of these three different equations - please pardon the bad merging!

Naturally, this has caused some confusion on what situations each of these equations apply to. Would one of these be more relevant to an interferometer — while another is for a single telescope? I'd like to share that these equations come from the textbooks "Foundations of Astrophysics" (Ryden & Peterson) and "Understanding Our Universe" (Palen, Kay & Blumenthal). If anyone has come across these equations, I'd be grateful for some advice on how to distinguish them (i.e. what situations or conditions they apply to).

> $$\theta\_\text{min}[\text{rad}] = 1.22 \frac{\lambda}{D}$$
> $$\theta = 2.06 \times 10^5 \frac{\lambda}{D}~\text{arcseconds}$$
>
> A telescope's resolution is determined by the ratio $\lambda/D$.

**Tags:** astrophysics, angular-resolution, interferometry

> **Comments:**
> **username_1**: Welcome to Stack Exchange! I've kept a link to the screen shot but written out the equation as a block quote using [MathJax](https://math.meta.stackexchange.com/q/5020/284619). Screen shots of text or equations are discouraged whenever the information can be written out explicitly. It helps in several ways; some people use screen text readers or other software, it can be easily copied and reused, and it can then be found using site searches.  
> **username_1**: @MikeG thanks for the fixer-upper. I attribute these glitches to "cosmic rays"  

---

## 2 answers

### Answer by username_2 on 2020-09-20. Score: 2

The expression $1.22 \frac\lambda D$ (in radians) represents the distance between the center of an Airy disk and the first minimum of an Airy disk that results from a perfect lens with a perfectly circular aperture and a perfectly focused point source. That assumes a bit too much perfection for some, who also see using the center of the first minimum as a bit generous. In those people's minds, it is best to reduce the factor of 1.22 to (approximately) one, resulting in $\frac\lambda D$ as the angular resolution.

Regarding the factor of $2.06\times10^5$ arc seconds, that is one radian.


---

### Answer by username_3 on 2020-09-20. Score: 1

$2.06 \times 10^5$ is the [radian arcsecond conversion](https://www.google.com/search?q=radian+arcsecond+conversion&oq=radian+arcs&aqs=chrome.3.69i57j0l7.12068j0j7&client=ubuntu&sourceid=chrome&ie=UTF-8), equal to $180 \times 60 \times 60 / \pi$ .

The $1.22$ is a geometrical factor applicable to circular apertures, as outlined in [Wikipedia](https://en.wikipedia.org/wiki/Angular_resolution#The_Rayleigh_criterion).


---

