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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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    綾羅飄起   posted on 2015/01/17
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