geek science

Can Legolas see that far?

In Lord of The rings, Legolas can count the exact number of horsemen five leagues (24 km) away and can also say that their leader is very tall. Minute Physics went on to investigate and see if such a thing is really possible.

In short words, no. This is because of diffraction as light is not a simple particle, it is a wave and it spreads out always like the waves of a lake. Given the diffraction phenomenon, the wavelength of the light and the diameter of the eye opening, we could calculate that at 24 km you can see objects that are smaller than 3 meters as a blurry disk called airy disk. You can’t distinguish things smaller than 3 meters at 24 km away with your naked eye. Legolas was surely using magic to see a more detailed picture of the horsemen. 😀

If you want to know how big should be the objects to see an airy disk of them at a distance use this formula:
0.007 ° * π /180 ° * dist = size. At 24 km objects smaller than 3 meters are seen as a three meter blob and objects that are at 40km distance and smaller than 4.9 meters across will be seen as blobs too. Neat, eh?

Where from do we have the 0.007 deg? That comes from the diffraction formula:
Θ = 1.22 * λ / d.
Θ is the diffraction angle
λ is the wavelength of light (usually 500 nm for green light is used for calculus)
d is the diameter of the eye opening (0.005 m)

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