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• 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.

There's a famous scene in the Lord of the Rings where the elf Legolas claims to be able

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B1 INT US light cm diffraction blurred size uv

# How Far Can Legolas See?

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