<p>One time I put a &quot;pinhole&quot; in some paper, it was roughly 5 or 10 mm and roughly round (I think I just pushed a pen through it) placed the paper over a flat household mirror, inclined the mirror so that it reflected the Sun through an open window and into a darkened area indoors where the resulting image was projected on to a white wall.</p>
<p>To calculate the expected performance I'll suggest using the technique of <a href="https://en.wikipedia.org/wiki/Similarity_(geometry)" rel="noreferrer">similar triangles</a> (see also <a href="https://en.wikipedia.org/wiki/Similarity_system_of_triangles" rel="noreferrer">Similarity system of triangles</a> for fun) and the <a href="https://en.wikipedia.org/wiki/Small-angle_approximation" rel="noreferrer">small angle approximation</a> and take the limit of the distance of the Sun being infinite.</p>
<p>If the angular width of the sun <span class="math-container">$\theta$</span> is say 0.5 degrees, that's roughly 0.01 radians. That means that the width of the sun's disk at a distance <span class="math-container">$L$</span> from a pinhole or any small aperture (transmission or reflection) will be the product <span class="math-container">$L \theta$</span>. If <span class="math-container">$L$</span> is 10 meters, then the height of the Sun's disk will be about 10 cm.</p>
<p>To get enough light through your aperture, it needs to be big enough. I recommend you have a series of apertures of different sizes available or some manipulable material like a simple sheet of paper where you can poke various size holes in it until you get satisfactory brightness.</p>
<p>Since rays from the Sun are essentially parallel, &quot;fuzziness&quot; of the image will simply be the aperture size <span class="math-container">$w$</span>, independent of distance.</p>
<p>So for a 0.5 cm aperture at 10 meters, you have a 10 cm solar disk which is &quot;fuzzy&quot; by 0.5 cm.</p>
<hr />
<p>Solar eclipse viewing via apodized mirror projection:</p>
<p><a href="https://i.sstatic.net/UrFsp.png" rel="noreferrer"><img src="https://i.sstatic.net/UrFsp.png" alt="solar eclipse viewing via apodized mirror projection" /></a></p>

CC BY-SA 4.0
2022-10-21T17:19:33.850Z
Using this, how far away from the screen should a 5-7 centimeters flat mirror be in order to provide a sharp image?
איתי מרלוב
CC BY-SA 4.0
2022-10-21T18:36:11.467Z
@איתימרלוב As uhoh's last paragraph says, the fuzziness depends on the aperture size. So if you don't cover the mirror, the image will be quite fuzzy, and you will need to use a huge distance to compensate for that.
PM 2Ring
CC BY-SA 4.0
2022-10-21T20:28:11.520Z
@איתימרלוב if you add a specific mirror to your question, I can update the answer to address it. That sounds too big unless you have a really long distance, and of course someone to keep moving the mirror. I'd recommend that you just give it a try on a normal sunny day and see what happens - that will likely be an "Aha!" experience, and you'l start using a mask over the mirror (paper with a hole in it) to improve the image sharpness at the cost of a dimmer image.
uhoh
CC BY-SA 4.0
2022-10-21T20:28:21.967Z
@איתימרלוב You'll also notice that you'll probably want to shade the screen from direct sunlight. Reflecting indoors through a door or window works best.
uhoh
CC BY-SA 4.0
2022-10-21T20:46:59.967Z
The mirror I currently have is 5 centimeters in diameter. I tried it with a distance of 10 meters and beyond and it seemed amazing, but of course I couldn't really tell from this far away from the casted image. I made some covers with varying apertures to test, but I need this to work at school so I'm not sure.
איתי מרלוב
CC BY-SA 4.0
2022-10-21T21:24:35.530Z
@איתימרלוב You will need 1) a way to keep the mirror steady without holding it. A bracket or just lean it against something, 2) an assistant to keep moving the mirror slightly and carefully as the sun moves. Remember that it moves its own diameter every 2 minutes, so if you don't want to always be adjusting your mirror to make the projection surface wide enough for a half-dozen sun diameters. Something to keep the mirror steady and an assistant will address "but of course I couldn't really tell from this far away from the casted image" because now you can be at the projected image.
uhoh
CC BY-SA 4.0
2022-10-21T01:13:44.773Z
2022-10-21T01:13:44.773Z
uhoh
<p>I plan on using flat mirror projection, among other methods, to view Tuesday's partial eclipse.
How do I calculate the distance my flat mirror has to be from my screen in order for it to cast a sharp, bright Sun image rather than its own shape or a blurred image?</p>

CC BY-SA 4.0
2022-10-20T20:26:06.873Z
The "throw" distance is ~100 times the diameter of the image. Your mirror should have an opaque mask over it with a small hole in it (~5 mm diameter). You really should test it beforehand, at approximately the same time of day as the eclipse. You will probably want to adjust the mirror angle over the course of the eclipse.
PM 2Ring
CC BY-SA 4.0
2022-10-21T17:19:40.390Z
This is a follow-on question to https://astronomy.stackexchange.com/q/50772/16685
PM 2Ring
CC BY-SA 4.0
2022-10-21T18:01:32.037Z
@PM 2Ring So the distance I need is about 100 times the size of the image I wanna get?
Would that be the case without covering the mirror as well?
איתי מרלוב
<observational-astronomy><amateur-observing><solar-eclipse><mirror>
How do I calculate my desired distance of mirror from screen?
איתי מרלוב
# How do I calculate my desired distance of mirror from screen?

(Asked by: username_0 on 2022-10-20)

I plan on using flat mirror projection, among other methods, to view Tuesday's partial eclipse.
How do I calculate the distance my flat mirror has to be from my screen in order for it to cast a sharp, bright Sun image rather than its own shape or a blurred image?

**Tags:** observational-astronomy, amateur-observing, solar-eclipse, mirror

> **Comments:**
> **username_1**: The "throw" distance is ~100 times the diameter of the image. Your mirror should have an opaque mask over it with a small hole in it (~5 mm diameter). You really should test it beforehand, at approximately the same time of day as the eclipse. You will probably want to adjust the mirror angle over the course of the eclipse.  
> **username_1**: This is a follow-on question to https://astronomy.stackexchange.com/q/50772/16685  
> **username_0**: @username_1 So the distance I need is about 100 times the size of the image I wanna get? Would that be the case without covering the mirror as well?  

---

## 1 answers

### Answer by username_2 on 2022-10-21. Score: 8

One time I put a "pinhole" in some paper, it was roughly 5 or 10 mm and roughly round (I think I just pushed a pen through it) placed the paper over a flat household mirror, inclined the mirror so that it reflected the Sun through an open window and into a darkened area indoors where the resulting image was projected on to a white wall.

To calculate the expected performance I'll suggest using the technique of [similar triangles](https://en.wikipedia.org/wiki/Similarity_(geometry)) (see also [Similarity system of triangles](https://en.wikipedia.org/wiki/Similarity_system_of_triangles) for fun) and the [small angle approximation](https://en.wikipedia.org/wiki/Small-angle_approximation) and take the limit of the distance of the Sun being infinite.

If the angular width of the sun $\theta$ is say 0.5 degrees, that's roughly 0.01 radians. That means that the width of the sun's disk at a distance $L$ from a pinhole or any small aperture (transmission or reflection) will be the product $L \theta$. If $L$ is 10 meters, then the height of the Sun's disk will be about 10 cm.

To get enough light through your aperture, it needs to be big enough. I recommend you have a series of apertures of different sizes available or some manipulable material like a simple sheet of paper where you can poke various size holes in it until you get satisfactory brightness.

Since rays from the Sun are essentially parallel, "fuzziness" of the image will simply be the aperture size $w$, independent of distance.

So for a 0.5 cm aperture at 10 meters, you have a 10 cm solar disk which is "fuzzy" by 0.5 cm.

---

Solar eclipse viewing via apodized mirror projection:

[![solar eclipse viewing via apodized mirror projection](https://i.sstatic.net/UrFsp.png)](https://i.sstatic.net/UrFsp.png)

> **Comments:**
> **username_0**: Using this, how far away from the screen should a 5-7 centimeters flat mirror be in order to provide a sharp image?  
> **username_1**: @איתימרלוב As username_2's last paragraph says, the fuzziness depends on the aperture size. So if you don't cover the mirror, the image will be quite fuzzy, and you will need to use a huge distance to compensate for that.  
> **username_2**: @איתימרלוב if you add a specific mirror to your question, I can update the answer to address it. That sounds too big unless you have a really long distance, and of course someone to keep moving the mirror. I'd recommend that you just give it a try on a normal sunny day and see what happens - that will likely be an "Aha!" experience, and you'l start using a mask over the mirror (paper with a hole in it) to improve the image sharpness at the cost of a dimmer image.  
> **username_2**: @איתימרלוב You'll also notice that you'll probably want to shade the screen from direct sunlight. Reflecting indoors through a door or window works best.  
> **username_0**: The mirror I currently have is 5 centimeters in diameter. I tried it with a distance of 10 meters and beyond and it seemed amazing, but of course I couldn't really tell from this far away from the casted image. I made some covers with varying apertures to test, but I need this to work at school so I'm not sure.  
> **username_2**: @איתימרלוב You will need 1) a way to keep the mirror steady without holding it. A bracket or just lean it against something, 2) an assistant to keep moving the mirror slightly and carefully as the sun moves. Remember that it moves its own diameter every 2 minutes, so if you don't want to always be adjusting your mirror to make the projection surface wide enough for a half-dozen sun diameters. Something to keep the mirror steady and an assistant will address "but of course I couldn't really tell from this far away from the casted image" because now you can be at the projected image.  

---

