Is the unit ‘one league’ used in LOTR (esp in elvish) the same as in our universe. Just asking as nobody here is questioning the units.
Yes. The books are all carefully translated from elvish and would have accounted for unit conversions.
I thought they were written by Bilbo and Frodo in Westron and later ‘translated’ by Tolkien
It depends on the atmosphere. On earth, the average ‘size’ of the atmospheric distortion experienced by a photon over 15 miles would far exceed the angular resolution of any pupil-sized aperture. This is a very simple explanation which groups a number of propagation effects broadly under the term “distortion.” Even without atmospheric distortion, there is a limit to the “information” a given aperture can resolve due to purely thermal noise. In theory, if you have an aperture temperature of absolute zero, the thermal resolution is infinite, but also then there is no process by which information can be generated by an I cident photon.
No, even without an atmosphere you have to contend with the diffraction-limited resolving power through an aperture (pupil), which is related to the diameter of the aperture and the wavelength of light.
A diffraction process is, mathematically, a fourier transform. A fundamental mathematical feature of a fourier transform is what’s known as the uncertainty principle.
Side note: you’ve probably heard of the special case of an uncertainty principle encountered in quantum mechanics frequently misattributed to the head of the Nazi nuclear program (Heisenberg), but this mathematical principle was actually well known for centuries beforehand, and the misattribution is mostly because of Nazi propaganda. We see it anywhere a fourier transform is used, from optics to orbital dynamics to quantum particles. This mathematical phenomenon is frequently miscited as quantum “weirdness” even though there’s nothing quantum (or all that weird) about it.
The pupil restricts the possible positions of incoming photons. A restriction in position increases the variance of momenta (for a photon, speed never changes, but the momentum vector can still change direction). A smaller pupil is more restrictive and causes the image to be blurrier as the incoming photons from each object you are trying to resolve. If you want to be able to resolve smaller angular sizes (small objects at large distances), you need a large aperture that reduces position restrictions on incoming photons and therefore diffraction-induced blurring due to momentum uncertainties.
Look up Airy diffraction for the special case of a circular aperture (e.g. a pupil or telescope).
Can he do interferometry and just have a 3rd but normal eye?
I mean, it’s a sunny day FFS!
Legolas actually vibrates very very quickly and is therefore performing synthetic aperture Interferometry, multiplying the size of his effective optical aperture.
I could be entirely wrong about this but isn’t it in-universe lore that Elves don’t see the curvature of the world and that’s how they can see so far?
