# 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