kawaiiiiiii

I feel it is very important to post this here:

The reason Legolas can see that far is because the curvature of Earth doesn't exist for elves. It is the same reason they can sail off into the Undying Lands without circling back around.
- If you get 50m above the ground and have nothing in the way, you can see 5 leagues away as well. Good luck counting individual people from that distance though. The anime eyes are a necessity
  
  That, or he’s got absolutely bonkers retinas that have truly incredible sensory density, and an absurdly developed visual cortex to support it.
  Argument basis: DSLRs. Compare the detail you can extract from a 1MP sensor to a 100MP sensor, shooting through the same optical setup at the same target.
- even if you ignore curvature you have a resolution limit that depends on the aperture. Look up Rayleigh criterion for more info
  
  But does it consider magic?
  
  Except that this problem doesn't specify distance between horseman, so I think it's a bit bogus --- no need to resolve an individual person to be able to tell that they're there. And for hair color, if you make assumptions about the clothes being worn, you could perhaps infer color of hair, even if the hair isn't resolvable (a person being a "single pixel" would have a different hue depending).
- Didn't Middle Earth lore say the Earth was flat, but was made spherical later? Had that happened by then?
  
  Yes, but it's not spherical for the elves, just the other races, which is why elven boats can sail to the undying lands, but human boats can't.
  
  the world was flat until numenor made war on the undying lands. at that point, numenor sank and the world was made round and the undying lands were placed somehow outside them, so that elves could still sail west along the straight way and get there, but everyone else just sailed west around the globe.
  later, tolkien changed his mind about a lot of this and played with it, trying to turn it into an always roundworld (scientifically accurate myth was his goal at this point) but couldnt really figure out how it'd work and he was old and then he died
- You mean the curvature of middle earth, right? RIGHT?!
  
  Middle Earth is canonically our Earth, in the past
- the curvature of Earth doesn't exist for elves
  Doesn’t it? Haven’t come across anything in Tolkien’s works that says this.
- How would that even work? Do time zones exist for everybody but elves? As the party travelled east, did Legolas start perceiving the sun to set later than it did for everybody else?
  
  If I remember correctly, the sun is the light of Valinor, so the sun actually never sets for Legolas (which is useful for seeing at night)
  edit: it might be the remaining silmaril being paraded around? either way, should always be visible to elves
- no, that's not why. it's because elves can just see better. it's the same reason they can walk on top of snow. they are slightly outside the laws that apply to ordinary humans. even aragorn is a hair over the line.

Some rough calculations:
5 leagues ≈ 15 mi ≈ 24.1 km. An average human has hair that's maybe 20 cm wide. Using the small angle approximation we get an angular size of 0.2/24100 ≈ 8.3x10^-6 radians.
At 400 nm wavelength, resolving details of that angular size requires an aperture of 1.22(400 nm / 8.3x10^-6) ≈ 5.88 cm.
So either Legolas has some absolutely massive eyes, has the ability to use both his eyes for optical interferometry (I'm voting for this since it's the coolest), or is just plain magic.
- There's magic in this world, it's possible elf sight is slightly magical.
- Adding from someone above. https://old.lemmy.world/comment/16391357
  
  didnt know old.lemmy was a thing.
  Thanks !
  
  Dang, that didn't federate to my instance. Their math seems to check out too.

If anyone was looking for the exact quote its from The Two Towers, Chapter 2 "The Riders of Rohan".
“’Riders!’ cried Aragorn, springing to his feet. ‘Many riders on swift steeds are coming towards us!’
“’Yes,’ said Legolas, ‘there are one hundred and five. Yellow is their hair, and bright are their spears. Their leader is very tall.’
“Aragorn smiled. ‘Keen are the eyes of the Elves,’ he said.
“’Nay! The riders are little more than five leagues distant,’ said Legolas.
“’Five leagues or one,’ said Gimli; ‘we cannot escape them in this bare land. Shall we wait for them here or go on our way?’
- So 5 leagues wasn't even the limit for him, he could have discerned their hair color at an even greater distance.
  
  I like the "lucky guess" theory. He's bullshitting them.

He has very strange-looking ears as well so I don't see the issue.
Also, take that, people who were whining about artists drawing manga-style LotR fanart after the Peter Jackson movies.
Anyway, does Legolas' ability to see very far necessarily mean his pupils must be humongous? The pupils on eagles aren't exactly very large either but as a cursory internet search tells me their internal structure is very different from human eyes. Anyone able to speculate on elvish eye anatomy?
- Your pupil is functionally the same as the aperture on a camera. Whenever light passes through an aperture, there is some diffraction that happens to it; the angle of the light changes. This is separate to anything the lens does. If there's too much diffraction, you won't be able to tell two different sources of light apart. The amount of diffraction depends on the wavelength of the light and the size of the aperture. Bigger apertures and shorter wavelengths diffract less. This "diffraction limit" has a formula accordingly.
  So for the question, we make some basic assumptions: take the wavelength of red light as it's the longest wavelength for visible light, and assume he needs to be able to tell apart two light sources 2 metres apart at a distance of 15 miles to distinguish individual riders. We figure out the angle between two points 15 miles away and 2 metres apart and now we know the angular resolution necessary. We know that the diffraction limit of Legolas' eyes has to be at least as small as that resolution. We also know our wavelength, so we can stick those into the formula and find out the minimum aperture (ie, the minimum diameter of Legolas' pupils to make out the riders at that distance)
  
  I'd argue that accurate color perception isn't necessary if one makes an assumption about the average age of the riders. Given that bright hair in humans is either blond or whitened by age (excepting albinos, which are rare), all of the riders having bright hair means that they're either blond or old. Assuming that there are few large groups of senior riders, Legolas could come to his conclusion based on brightness alone.
  Unfortunately I don't know enough about optics to say whether this makes any difference.
- I don't know enough about eyeballs to be able to answer, but 5 leagues is a bit more than 5x farther than eagles can see, and eagles already have larger pupils than humans do.
- Yes, the ability to see very far away does imply in very large eyes if you define "see" by properly focusing on the objects. But not large pupils, what matters is the size of the eyes lenses, on the bare front of them.
  But no, he could be able to perceive those stuff without the larger eyes if he had a good mental model of how the horsemen interfere with the background (what is probably easier than it seems, because they would be moving), and how their hair would interfere with the previous outline.
  
  You ninja'd me lol. but that's a good point about the interference.
- many eyes are near the diffraction limit (for human sized eyes the diffraction limit is around 20/10 vision). To have better accuity you factually need larger eyes. Although it's the size of the lens that matters more than pupil size strictly. The pupil modifies the lens optics but the lens determines the limit.
  
  What if the refractive index of elvish eyes were somehow absurdly high? Paired with a very high resolution and sensitivity retina of course.

3.5 cm pupils? I've heard of "wide-eyed" but this is ridiculous!
But I never knew a "league" was 3 miles. That's like, a lotta football fields!

Ok but 15 miles is over the horizon isn't it?
- Yes, but it doesn't mention that he's 30ft tall. That might make 3.5cm pupils proportional.
- Elves canonically see in a flat plane, which is why they're able to navigate to Valinor across the straight road, which is west of the grey havens ignoring the world's curvature.
  
  Bros' eyes make light curve

With coherent detection I think the separation between eyes would allow for this.

Middle Earth is flat. When they sail to the Undying Lands, they actually just fall off the edge.

Remember kids: it it uses US American rando units, it’s probably not science!

i would just like to mention that the physics of the universe in LOTR are obviously very different, since you can sometimes see stars during the day, if you're in a deep valley

Not science (but related to huge eyes) but I recently learned that in The Sims 2 you can push the body control sliders to their max, hit a button to normalize the sliders while keeping your changes and then max out the sliders again, so you can do shit like give your sims Galaxy sized eyeballs.
- i remember doing this to make a sim with a nose the size of a car. I named him Nostrildomus.