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.
I think the pupil size calculation is based on defraction, so it doesn't matter how dense your retina is, if your pupils are smaller than that you still wont see enough detail. This is one of the reasons why we keep building bigger telescopes and especially telescope arrays. The bigger the effective apeture, the finer the detail it can resolve.
Honestly, I’m waiting with bated breath until we as a global society can get our shit together enough to create a massive system-wide observation cluster. The shit we’ll learn from that will undoubtedly be incredible. I want my fully automated post-scarcity hedonistic space communism society. But I guess we have to get through the Great Filter first :/
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).
So, a typical pupil is around 2 mm in diameter in bright conditions. With the Rayleigh limit that results in an angular resolution of 1.22 * 60010^-9 m / 210^-3 m = 3.66*10^-4 rad
At a distance of 5 x 3 mi = 15 mi = 24.1 km this corresponds to a point to point distance of
tan(a/2) = (d/2)/l
d = tan(a/2) * l * 2 = tan(3.66*10^-4) * 24100 * 2 = 8.8 m
So in conclusion, with regular, human-like eyes he could discern points that are at least 8.8 m apart in the best case scenario. Discerning hair color from the color of the clothes would need a much higher resolution, and the horsemen are probably not 10 m apart from each other either. And again, this is a theoretical limit, real-world resolution would probably be significantly lower.
which is why legolas has huge anime eyes
That's part of the "make appropriate estimates" bit. You can just pick any reasonable number for the angular resolution Legolas needs and answer the question using that. Provided you do the method right, you'll get the marks.
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.
Wait, is it the boat that ignores the spherical attribute or the entity that commands the boat?
Can an elf sail to the undying lands commanding a human built vessel?
I think you have to be an elf building a ship and convince each plank individually that the world is flat
It's neither, it's the Will of Eru Illuvatar that determines whether you can travel the Straight Road or not. Ælfwine travelled the Straight Road and landed at Tol Eressëa in 869AD after fleeing the Danes, and he was a Man, not an Elf.
Eru damn tangential elves flying off into space.
This gives strong "Lovecraft describing things he doesn't understand as noneuclidian" vibes.
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
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.
His thought process was probably "we're gonna run away anyways, I'm gonna tell these idiots I can see their hair color lol"
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.
I feel it is very important to post this here:
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.
Legolas can also tell that they carry spears and their leader is taller than average. Spectral information is unlikely to tell him that.
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.
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.
Remember kids: it it uses US American rando units, it’s probably not science!
Middle Earth is flat. When they sail to the Undying Lands, they actually just fall off the edge.
With coherent detection I think the separation between eyes would allow for this.
Okay all you generative AI image hobbyists, let's see Legolas with big, shiny eyes!
as if humans haven't already drawn anime legolas
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