Meanwhile I am trying to think of the shape that gives a further focal point

3.5 cm pupils? I've heard of "wide-eyed" but this is ridiculous!

But I never knew a "league" was 3 miles. That's like, a lotta football fields!

I remember somebody making the argument that due to the diffusion of light he would not be able to discern their features at all.

I feel it is very important to post this here:

Some rough calculations:

5 leagues ≈ 15 mi ≈ 24.1 km. An average human has hair that's maybe 20 cm wide. Using the small angle approximation we get an angular size of 0.2/24100 ≈ 8.3x10^-6 radians.

At 400 nm wavelength, resolving details of that angular size requires an aperture of 1.22(400 nm / 8.3x10^-6) ≈ 5.88 cm.

So either Legolas has some absolutely massive eyes, has the ability to use both his eyes for optical interferometry (I'm voting for this since it's the coolest), or is just plain magic.

With coherent detection I think the separation between eyes would allow for this.

Remember kids: it it uses US American rando units, it’s probably not science!

i would just like to mention that the physics of the universe in LOTR are obviously very different, since you can sometimes see stars during the day, if you're in a deep valley

If anyone was looking for the exact quote its from The Two Towers, Chapter 2 "The Riders of Rohan".

“’Riders!’ cried Aragorn, springing to his feet. ‘Many riders on swift steeds are coming towards us!’
“’Yes,’ said Legolas, ‘there are one hundred and five. Yellow is their hair, and bright are their spears. Their leader is very tall.’
“Aragorn smiled. ‘Keen are the eyes of the Elves,’ he said.
“’Nay! The riders are little more than five leagues distant,’ said Legolas.
“’Five leagues or one,’ said Gimli; ‘we cannot escape them in this bare land. Shall we wait for them here or go on our way?’