Chad Orzel’s got a great post up about the physics of Lord of the Rings. It’s about Legolas the elf and his excellent eyesight. His eyes are so good that in fact they’re probably operating well beyond the physical diffraction limits of any optical device with a human-sized pupil. Some speculation was discussed about how his eyes might plausibly be so good without magic: maybe he can see in the short-wavelength UV, maybe he can do interferometry(!), maybe elf pupils are bigger than we think, maybe the Middle Earth “league” is shorter than our identically-named unit of distance, along with a few other interesting suggestions. “It’s magic” is probably the right answer, but then we miss the fun of a physics discussion.
I have another thought. Why doesn’t anyone just use a telescope or binoculars? Ok sure, it’s ancient middle earth and presumably a Galileo hasn’t been born yet. But I see no reason that this ought to stop them. Middle Earth is not a completely pre-technological environment, there’s science of some sophistication. Let’s see:
Glassworking: Good enough to produce Palantir, which are crystal spheres used for communication and surveillance. There’s also very considerable skill in gem cutting, which is important in The Hobbit.
Metallurgy: At least to the medieval level given all the sword-reforging and such, and probably much better since they can work with the practically indestructible Mithril. We’re leaving aside the whole ring-forging thing since that seems to be closer to magic than science.
Chemistry: It’s unclear how much theory they actually understand, but as a practical matter they’ve at least got gunpowder figured out. Nobody uses it but Saruman, which is a shame. Mining the Pelanor Fields might have saved our heroes a lot of trouble. I don’t remember if the metal of the swords is mentioned specifically, but if it’s steel as opposed to iron then that probably adds to the sophistication of the people of Middle Earth with respect to both chemistry and metallurgy.
Biology: Given that the flora and fauna of Middle Earth is so far removed from our experience it’s hard to be definitive about this. The orcs and Uruk-Hai are both arguably bioengineered, but this seems to have been done with magic rather than purely genetic means.
So despite the fantasy setting I’d say the characters have access to an early and little-developed but still considerable quantity of scientific knowledge. If Gondor had spent some of its money on an ancient Los Alamos the whole thing might have been a lot easier.