There's a famous scene in the Lord of the Rings where the elf Legolas claims to be able
to count the exact number of horsemen 5 leagues away, and on top of that can tell that their
leader is very tall. But even with the most perfect eyes possible, would anyone be able
to see that far?
When we see, we're looking at light that's traveled outwards from a light source, bounced
off an object, passed through the lens in the eye, and been focused into an image on
the retina. Except... light isn't a particle traveling in perfectly straight lines - it
is a wave. And therein lies the problem, both for us, and for Legolas.
Because any wave - whether water, sound or light - that travels through a small opening
will become spread out by a process known as diffraction, which for light, essentially
blurs the image.
You can see this with a telephoto camera lens where the camera aperture has been made very
very small - small details in the photograph start to become spread out, blurred, and even
indistinguishable! Or, if you hold the edge of a piece of paper in front of your eye and
try to read past it, small words will become blurry!
The blur that a small point of light spreads out to become is called an Airy disk, and
the size of the Airy disk for distant tiny objects depends only on the wavelength of
light in question and the size of the opening you're looking through. So for visible sunlight
and a human-sized pupil, diffraction limits us to at best be able to distinguish objects
that are bigger than seven one-thousandths of a degree, for example, an object one centimeter
in size a hundred meters away,. Another way of putting this is that everything 100m away
and smaller than 1cm gets blurred so that it appears to be about 1cm in size, no matter
how small it really is - subtle details smaller than 1cm blur away.
So when Legolas, who has very human-sized pupils, looked at the riders of Rohan 24 km
away, diffraction tells us that everything smaller than 3 METERS would have been blurred
to about three meters in size - perhaps he could still count the number of horsemen,
but he definitely couldn't distinguish their heights to within a few centimeters...
Unless Legolas could see in ultraviolet. Shorter wavelength light diffracts less, so if he
could see in the extreme UV, then he'd be able to distinguish objects 10 cm in size,
almost enough to discern the height of a man.
Except that pretty much any kind of air absorbs extreme UV light - so even if he could see
UV, Legolas would have been left in the dark. Or maybe it's just... magic.