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.