this post was submitted on 01 Aug 2025
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[Edit: no. The λ in question is the wavelength of the light before it reaches the pupil because that wavelength is what determines how many more wavelengths light has to travel from the source to reach one side of the pupil than the other. The lens and vitreous humour focus the light onto the retina by ensuring that the light from a point source travels the same amount of time to reach the corresponding point on the retina, regardless of which point on the pupil it passes through. Because all the light travels the same amount of time from the source to the corresponding point on the retina, the light waves’ maxima all arrive at the same time, so the light waves interfere constructively at that point and produce a bright spot. Near that point, the light travels almost, but not quite, the same amount of time, so the point source illuminates a region around the point slightly less than it illuminates the point where it is focused. When light comes from two sources close to each other, the difference between the amount of time the light from one source takes to reach one side of the pupil and the amount of time the light from the same source takes to reach the other side of the pupil is close to the difference between the amount of time the light from the second source takes to reach one side of the pupil and the amount of time the light from the second source takes to reach the other side of the pupil. And there is nothing that the lens or vitreous humour can do about that.]

In The Two Towers, the elf Legolas, at a distance of five leagues, observed once, “there are one hundred and five [riders on horses]. Yellow is their hair, and bright are their spears. Their leader is very tall.” In 2014, a viral video made the claim that this was impossible, based on the equation θ≈1.22λ/d, where θ is the angular size of the Airy disk produced by a point source of light, λ is wavelength, and d is the diameter of the pupil. My idea is that, in a material with a high refractive index, λ would be proportionally less than it is in air, resulting in a smaller θ, and with it an image with better resolution.

(This post’s image and alt text are not my work; Wikipedia user Inductiveload released them into the public domain.)

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[–] MotoAsh@lemmy.world 10 points 1 week ago* (last edited 1 week ago)

The real world is seldom as simple as the maths, but several animals do see much better than humans. In particular hunting birds.

A biologist might have to chime in on this one, as it might genuinely come down to rod/cone density and other factors as well.

[–] ladel@feddit.uk 2 points 1 week ago

I think yes (just use lamda/n in place of lamda). I seem to remember diamond has one of the highest n in visible (while still transparent), so it might be difficult to imagine it could be higher than that. Alternatively, why not say Legolas can see in the ultraviolet to get lamda down.

[–] FlowVoid@lemmy.world 2 points 1 week ago* (last edited 1 week ago) (1 children)

The Airy disk is caused by diffraction at the entrance pupil to the lens. Even a perfect lens would be affected. The vitreous humor (which is behind the lens) cannot restore image degradation that already occurred when light passed the pupil.

[–] a_g_marut@lemmy.world 1 points 1 week ago

This is the best answer because it narrows down the problem to the outside of the eyeball.

I mean, there is magic in lord of the rings, so I’m sure their physics and chemistry systems have some oddities that our world does not