<p>This is a first-order approximation, and works well for simple models of irradiation of the atmosphere or the Earth's surface.</p>

<p>But, a simple experiment with a pinhole camera or a single lens will show that this model doesn't work in imaging situations.  The sun is an "extended object," meaning it is not a point source, so the image you get is not what you would expect from a point source.  Worse, even if the sun were a point source, the distance to the geometric focal point is different very slightly from the distance if all the sun's rays were perfectly parallel.  See the Lensmaker's Formula,  <span class="math-container">$ \frac{1}{f} = \frac{1}{p} + \frac{1}{q} $</span> where p and q are the distances from the lens to the source and the image respectively.   (I'll warn that for a reasonable lens, say focal length <span class="math-container">$ f = 10 m$</span>, the difference between focal location for rays that are parallel and rays from a point source <span class="math-container">$150\space million\space km$</span> away is ridiculously small) </p>

<p>Similarly, if you want to model the umbra and penumbra during a solar or lunar eclipse, you'll need to take the physical extent of the sun into consideration.  </p>

CC BY-SA 4.0
2019-02-25T20:06:05.973Z
2019-02-25T20:06:05.973Z
Carl Witthoft
<p>There isn't a better way to conceptualize this, because that's how it happens. The sun is very large and very far away, so the rays reaching us are effectively parallel to one another. This is already the best way to conceptualize how light strikes the earth - if there were a better one, you probably would have heard about it instead of this way.</p>

CC BY-SA 4.0
2019-02-25T20:06:43.330Z
Well, we **have** heard of a better way.  The "plane-parallel"  model has limited utility.
Carl Witthoft
CC BY-SA 4.0
2019-02-25T15:29:58.203Z
2019-02-25T15:29:58.203Z
Nuclear Hoagie
<p>Most diagrams I see of sunlight look like something like this:</p>

<p><a href="https://i.sstatic.net/vkTLX.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vkTLX.png" alt="enter image description here"></a>.</p>

<p>They show that for basic geometric analyses, the sun's radiation can be thought of as 'thin lines' that strike earth. Further, at an equinox, those rays strike hit the horizon of every point on earth (except the poles) directly from the east. So, the diameter for the earth does not matter at all it terms of the angle at which the rays strike.</p>

<p>I'm curious - how far will this conceptual frame take me? What is a better way to conceptualize how the sun's light strikes the earth?</p>

CC BY-SA 4.0
2019-02-25T16:26:37.693Z
What you describe sounds pretty reasonable to me, if I understand correctly. I think you have come across what's called [ray tracing](https://en.wikipedia.org/wiki/Ray_tracing_(graphics)) and it's one standard way to simulate illumination in all kinds of fields including computer graphics and rendering. If you can think of some effect that wouldn't work or problems that you might encounter, you can refine your question or ask a new one (if it's still somewhat related to astronomy). For example, how bright is sunlight in Watts per square meter as a function of latitude, etc.
uhoh
<positional-astronomy><sun-rays>
How should I think about sunlight for the purposes of analyzing the angles it makes w/ earth?
Hayden
# How should I think about sunlight for the purposes of analyzing the angles it makes w/ earth?

(Asked by: username_0 on 2019-02-25)

Most diagrams I see of sunlight look like something like this:

[![enter image description here](https://i.sstatic.net/vkTLX.png)](https://i.sstatic.net/vkTLX.png).

They show that for basic geometric analyses, the sun's radiation can be thought of as 'thin lines' that strike earth. Further, at an equinox, those rays strike hit the horizon of every point on earth (except the poles) directly from the east. So, the diameter for the earth does not matter at all it terms of the angle at which the rays strike.

I'm curious - how far will this conceptual frame take me? What is a better way to conceptualize how the sun's light strikes the earth?

**Tags:** positional-astronomy, sun-rays

> **Comments:**
> **username_1**: What you describe sounds pretty reasonable to me, if I understand correctly. I think you have come across what's called [ray tracing](https://en.wikipedia.org/wiki/Ray_tracing_(graphics)) and it's one standard way to simulate illumination in all kinds of fields including computer graphics and rendering. If you can think of some effect that wouldn't work or problems that you might encounter, you can refine your question or ask a new one (if it's still somewhat related to astronomy). For example, how bright is sunlight in Watts per square meter as a function of latitude, etc.  

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## 2 answers

### Answer by username_2 on 2019-02-25. Score: 1

This is a first-order approximation, and works well for simple models of irradiation of the atmosphere or the Earth's surface.

But, a simple experiment with a pinhole camera or a single lens will show that this model doesn't work in imaging situations. The sun is an "extended object," meaning it is not a point source, so the image you get is not what you would expect from a point source. Worse, even if the sun were a point source, the distance to the geometric focal point is different very slightly from the distance if all the sun's rays were perfectly parallel. See the Lensmaker's Formula, $ \frac{1}{f} = \frac{1}{p} + \frac{1}{q} $ where p and q are the distances from the lens to the source and the image respectively. (I'll warn that for a reasonable lens, say focal length $ f = 10 m$, the difference between focal location for rays that are parallel and rays from a point source $150\space million\space km$ away is ridiculously small)

Similarly, if you want to model the umbra and penumbra during a solar or lunar eclipse, you'll need to take the physical extent of the sun into consideration.


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### Answer by username_3 on 2019-02-25. Score: 0

There isn't a better way to conceptualize this, because that's how it happens. The sun is very large and very far away, so the rays reaching us are effectively parallel to one another. This is already the best way to conceptualize how light strikes the earth - if there were a better one, you probably would have heard about it instead of this way.

> **Comments:**
> **username_2**: Well, we **have** heard of a better way.  The "plane-parallel"  model has limited utility.  

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