this post was submitted on 23 Jun 2024
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I took some antenna theory courses back in the day and yes, you are correct. Some frequencies reflect off the upper atmosphere so there would be a longer effective range at higher incident angles (going into the top of the head) but it wouldn't completely block radio waves. Going from memory, the wavelengths that reflect off the upper atmosphere are long enough that a tin foil hat wouldn't cause much interference anyways.
TLDR: Fashionable, but not practical.
Just to add - this "hat" would also likely improve reception.
Certainly could if it had good contact. If it was air gapped (held up by hair), it could be an effective barrier for shorter wavelengths.
Lower frequencies (like the HF range) can propagate further due to reflection/refraction with the earth and the ionosphere. Increasing the frequency can lead to e-skip and troposhpeheric ducting. But even the HF range has shorter wavelengths than our brains, which operate in much lower frequencies (Hz vs MHz). So you would think that our brainwaves would pass through tin-foil much more easily
But it's the tin-foil's electro-conduction that "foils" the electromagnetic waves' (i.e radio waves') ability to pass through it. But you would have to have no gaps in the tin-foil to completely block all waves from passing through. So like, an entire foil suit or a walking Faraday cage.
TL;DR - it's not about the length of the electromagnetic wave, it's the electro-conduction (insulating) property of the tin-foil that matters