Friday, August 04, 2017

Perspective: Why Don't Sunbeams Look Parallel?

Not too long ago, I had an internet run-in with a "flat Earth" type who hit me with an argument I'd never heard before: the sun, they insisted, is actually only a few hundred miles from Earth, as can be proven with some simple mathematical analysis of sunbeams. By measuring the apparent angle between sunbeams striking the opposite sides of a valley that they knew the width of, they could trace back and use geometry to calculate how far away the source must be! I want to share this little anecdote because it's a great reminder of how important a diverse and well-rounded education is: someone with training in visual arts would never have missed the error that this person made.

Rays of sunlight filter through a forest canopy, scattering off particles of mist to become visible.

Let's look closely at the above image. The distance between the highest visible sunbeam, at the point where it passes the large tree on the left side of the picture, and the ground looks to be about forty feet, tops. (We don't need terribly precise numbers here, and you'll see why in a moment.)

Now let's look at the apparent angle between that high sunbeam and the one that strikes the ground at the base of that tree. If you hold up the corner of a piece of paper to your screen, you can see that the spread between those two rays is close to a right angle, 90 degrees!

So something's clearly not right here. If we do the math, treating the tree as the 40-foot-long hypotenuse of a right triangle, the Pythagorean theorem tells us that the sun is sitting squarely in this grove of trees with the photographer.

"Something's not right here; according to my calculations, I should be on fire."

Depending on the scene you analyze this way, you can find the sun to be a stone's throw away, or a few thousand miles—and every number you get will be as wrong as the last. It's a fact you learn in many introductory physics classes: that any photon from the sun that hits Earth is traveling almost perfectly parallel to every other one. This is due in part to the size of the sun, but mostly to the distance between here and there—if two photons are even a fraction of a degree off from one another in their initial trajectories, they'll be several Earth-widths apart by the time they've covered the ~92 million miles from the sun to Earth's orbital radius. So perhaps it's no surprise that an outside-the-box thinker with a head for numbers could look at what they see and come to the conclusion that there's a disconnect between what they've been taught and what they observe.

But this is where a little bit of artistic training would come in handy: the apparent spread between sunbeams isn't actual spread; it's an effect of perspective, as the following photo demonstrates perfectly:
If these train tracks actually converge the way they appear to, someone's going to be in a lot of trouble.

All that's happening here—and in the sunbeam image above—is that the objects in the image appear smaller the further away they are. And not just objects, but distances, too: the further away down the tracks you go, the smaller the gap between them seems, creating the appearance that they come together at a point in the far-off distance. In graphic design and art, this point is called the vanishing point.

Of course, as internet arguments tend to go, explaining all this didn't help much...the commenter called me a sheep or something and proclaimed that, if what I said were true, buildings at a distance would appear to have an angle to them rather than standing vertically upright.

Regardless, it's a fun lesson about the intersection of art and physics, worth having in your pocket next time someone tries to tell you that arts education isn't important...or that the sun is only a few hundred miles away.

Stephen Skolnick

7 comments:

  1. perhaps you could have told him/her to simply draw an elongated greater-than sign (>) on a piece of paper and then look at it from the edge of the page from the open side and note how the apparent angle seems to change.

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  2. HI, I am not sure you're explanation is worth the paper its written on. I've seen local heat spots from the sun from high altitude balloon footage, I've seen no curve what so ever, unless I'm watching video with a fish eye. I also understand perspective and how the horizon works. You're mumbo jumbo its just silly you actually believe it though, either that or you like the sound of you're own voice?? sorry but thanks for the effort, the earth is not a spinning ball.

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  3. If you visit the Mr. thrive and survive YouTube channel, you will find that your answer is not sufficient. Parallel items do not spread apart or come together in the distance. If that was the case, if you saw buildings on the horizon from a distance city they would all converged towards one another at the tops. There is a video posted recently on the channel above where clouds are used to show shadows from an airplane. The shadows on the clouds are at all different directions which is impossible for a son that is 93,000,000 miles away. The answer for perspective is correct in some instances but not in this one. It is an incomplete picture of how perspective works. Like I said, buildings in the distance would appear to have their tops face each other the further way they were and we never observed this with parallel items. The sun is close and there are many many proofs of this. Please check it out for yourself I'm glad you're doing thinking.

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  4. Dear Stephen, although perspective has its place, with objects which start out parallel in the distance do NOT spread out as they approach the user (the train tracks don't work in reverse - they never go beyond parallel as they approach you). This is easily noted when you see the site of a downtown city with skyscrapers in the distance. If perspective made those parallel buildings do as you say here, the tops of the buildings would appear to converge and almost touch in the distance. This does not happen. An object that starts parallel in the distance does not spread out as they approach you - ever!

    A video link below will show you that a picture of clouds taken from an aircraft shows that the shadows themselves indicate a close sun - in this case, the shadows don't all approach you. Ther are several proofs tht the sun is not only close, but that we don't see it directly (a rainbow needs two reflectors to occur as science can't reproduce one indoors unless two reflectors are used. Outdoors, rain is one reflector. The sun must be something like glass for the other. That is not the only reason why it can be shown the sun is close and that we don't see it directly. YOu are thinking which is a good thing. Most people simply reject and scoff and never learn anything. All the best. Rich

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  5. Wow, this Rich guy didn't even understand the article, or like typical flat earthers, didn't read it. "Hot spots" on clouds. LOL, that is because the Earth is round and the sun reflects at the incident angle. What an idiot.

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  6. The angles of apparent sunbeams are due to the objects' interruption of the beams. Your perception of vanishing point is an effect of perspective and distance from YOU. The nature of vanishing point has nothing to do with the distance of the light source.

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  7. I'm guessing Rich and "Mr. Thrive and Survive" are one and the same. Wouldn't be surprised that this is an attempt to promote a Flat Earth Channel.

    He parroted a video making fun of a Washington Post video where they tongue-in-cheek attempt to answer a "Dear Science" question about why solar eclipses move west to east if the moon goes from east to west. At first I was questioning it myself. But a little effort yielded that there was a glaring error in the question itself: The moon actually rotates COUNTER clock-wise around the earth....meaning it goes west to east.

    Either Rich (Mr. Thrive and Survive I presume?) either missed that or he chose to ignore it to get more views and make more money like a lot of these Flat Earth Snake Oil salesmen do.

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