Imagine I'm on a rooftop of a building. If I am lying down behind a wall and cannot see someone standing on another building- no matter which direction I look, is it possible that they can see me?
[Physics] Line of vision – If I cannot see someone, is it possible that they can see me
visible-lightvision
Related Solutions
Binoculars include a prism that invert the image as the lenses already do an inversion. The lens apparatus would be a bit heavy to use as an inversion mechanism, but the prisms (Porro prims for instance) could do the job. They can provide a decent field of view. Even if they take some space and weight, I doubt any other apparatus, such as a lens arrangement, could do better.
Fun question!
As you pointed out,
$$\theta \approx 1.22\frac{\lambda}{D}$$
For a human-like eye, which has a maximum pupil diameter of about $9\ \mathrm{mm}$ and choosing the shortest wavelength in the visible spectrum of about $390\ \mathrm{nm}$, the angular resolution works out to about $5.3\times10^{-5}$ (radians, of course). At a distance of $24\ \mathrm{km}$, this corresponds to a linear resolution ($\theta d$, where $d$ is the distance) of about $1.2\ \mathrm m$. So counting mounted riders seems plausible since they are probably separated by one to a few times this resolution. Comparing their heights which are on the order of the resolution would be more difficult, but might still be possible with dithering. Does Legolas perhaps wiggle his head around a lot while he's counting? Dithering only helps when the image sampling (in this case, by elven photoreceptors) is worse than the resolution of the optics. Human eyes apparently have an equivalent pixel spacing of something like a few tenths of an arcminute, while the diffraction-limited resolution is about a tenth of an arcminute, so dithering or some other technique would be necessary to take full advantage of the optics.
An interferometer has an angular resolution equal to a telescope with a diameter equal to the separation between the two most widely separated detectors. Legolas has two detectors (eyeballs) separated by about 10 times the diameter of his pupils, $75\ \mathrm{mm}$ or so at most. This would give him a linear resolution of about $15\ \mathrm{cm}$ at a distance of $24\ \mathrm{km}$, probably sufficient to compare the heights of mounted riders.
However, interferometry is a bit more complicated than that. With only two detectors and a single fixed separation, only features with angular separations equal to the resolution are resolved, and direction is important as well. If Legolas' eyes are oriented horizontally, he won't be able to resolve structure in the vertical direction using interferometric techniques. So he'd at the very least need to tilt his head sideways, and probably also jiggle it around a lot (including some rotation) again to get decent sampling of different baseline orientations. Still, it seems like with a sufficiently sophisticated processor (elf brain?) he could achieve the reported observation.
Luboš Motl points out some other possible difficulties with interferometry in his answer, primarily that the combination of a polychromatic source and a detector spacing many times larger than the observed wavelength lead to no correlation in the phase of the light entering the two detectors. While true, Legolas may be able to get around this if his eyes (specifically the photoreceptors) are sufficiently sophisticated so as to act as a simultaneous high-resolution imaging spectrometer or integral field spectrograph and interferometer. This way he could pick out signals of a given wavelength and use them in his interferometric processing.
A couple of the other answers and comments mention the potential difficulty drawing a sight line to a point $24\rm km$ away due to the curvature of the Earth. As has been pointed out, Legolas just needs to have an advantage in elevation of about $90\ \mathrm m$ (the radial distance from a circle $6400\ \mathrm{km}$ in radius to a tangent $24\ \mathrm{km}$ along the circumference; Middle-Earth is apparently about Earth-sized, or may be Earth in the past, though I can't really nail this down with a canonical source after a quick search). He doesn't need to be on a mountaintop or anything, so it seems reasonable to just assume that the geography allows a line of sight.
Finally a bit about "clean air". In astronomy (if you haven't guessed my field yet, now you know.) we refer to distortions caused by the atmosphere as "seeing". Seeing is often measured in arcseconds ($3600'' = 60' = 1^\circ$), referring to the limit imposed on angular resolution by atmospheric distortions. The best seeing, achieved from mountaintops in perfect conditions, is about $1''$, or in radians $4.8\times10^{-6}$. This is about the same angular resolution as Legolas' amazing interferometric eyes. I'm not sure what seeing would be like horizontally across a distance of $24\ \mathrm{km}$. On the one hand there is a lot more air than looking up vertically; the atmosphere is thicker than $24\ \mathrm{km}$ but its density drops rapidly with altitude. On the other hand the relatively uniform density and temperature at fixed altitude would cause less variation in refractive index than in the vertical direction, which might improve seeing. If I had to guess, I'd say that for very still air at uniform temperature he might get seeing as good as $1\rm arcsec$, but with more realistic conditions with the Sun shining, mirage-like effects probably take over limiting the resolution that Legolas can achieve.
Best Answer
The basic answer to your question is "no, absent weird effects like exotic polarized fields", but it's worth noting that when the sun is fairly low and one person is "upsun" and the other is "downsun", and they are looking at each other, the "downsun" person will appear sharp and crisp with all colors and details standing out brightly, while the "upsun" person will be a dark silhouette surrounded by blinding glare. People forget this all the time, and think each can see the other equally well. That's why the eastbound drivers don't bother to turn on their headlights at sunset, even though the oncoming westbound drivers are squinting like crazy into the glare and can barely discern anything at all.