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.
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.
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.
the diffraction limit of a lens cant really be circumvented optically, it’s a fundamental limit of light due to being waves. so some insane refractive index wont help.
but elves are magical, so what if their eyes don’t care about the physical nature of light and just sorta convert it to magical pseudo-light when it contacts their tissue?
Aye but light, being a wave, doesn’t travel at the same speed in every medium. In a high refractive index media the wavelengths of visible light would be shorter. Would this not reduce the effect of diffraction on them for normal-sized pupils?
The light diffracts before it reaches the lens so this wont help. Also, refraction doesnt change the wavelength of light, it just takes time to bounce and re-emit through the medium.
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.
Someone did the math above.
https://old.lemmy.world/comment/16391357
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.
Unfortunately neither do I! It has been a long time since I studied physics, and I never did optics
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.
the diffraction limit of a lens cant really be circumvented optically, it’s a fundamental limit of light due to being waves. so some insane refractive index wont help.
but elves are magical, so what if their eyes don’t care about the physical nature of light and just sorta convert it to magical pseudo-light when it contacts their tissue?
that’s not really relevant to the question at hand. “but magic” is clearly not an interesting answer when people are playing around with physics.
Aye but light, being a wave, doesn’t travel at the same speed in every medium. In a high refractive index media the wavelengths of visible light would be shorter. Would this not reduce the effect of diffraction on them for normal-sized pupils?
The light diffracts before it reaches the lens so this wont help. Also, refraction doesnt change the wavelength of light, it just takes time to bounce and re-emit through the medium.