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
he 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.
因为任何波 无论是水波 声波还是光 当它
Because any wave – whether water, sound or light
traveling 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.
So this video is brought in part by audible.com,
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If you go to audible.com/minutephysics
you can try out audible by downloading a free audio book of your choice like
The Two Towers the second book in J.R.R. Tolkien
excellent but potentially physically inaccurate the Lord of the Rings trilogy.
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