Does the Mage Hand cantrip pass through solid surfaces?

Last session, my Arcane Trickster was faced with some murky water and we needed to know how deep the bottom was. I decided to use mage hand to try to locate the bottom of the water without putting my own hand in there, but then we were stuck with the question: would my mage hand just float straight through the bottom?

Another way of wording this question would be “does mage hand go through walls”?

The spell says:

A spectral, floating hand appears at a point you choose within range.

But exactly what the hand is is not described any further. Does spectral mean “float through walls” like an incorporeal ghost, or is it spectral only in the sense that it’s not a creature or an object? Either way, if the caster sent the hand through a wall or the floor, would it go through or just bump up against the wall?