I imagine that the piece you are playing has an F# somewhere in the measures before it. A practiced ear will expect that F# to still be there later on - it's not so much "known" theory as patterns that are sensed.
A closer look at the graphic might be warranted.
Can you explain?
I don't understand why there is a natural sign in front of the F in bar 3 in the "Venetian Gondola Song" by Mendelssohn? The key-signature doesn't have a flat (nor a sharp) for the F and there are no other accidentals before the natural.
Your conclusion concerning the significance of the superfluous accidental ("I imagine that the piece you are playing has an F# somewhere in the measures before it. A practiced ear will expect that F# to still be there later on") was based on a misapprehension of its context:
I can't know it's context. There are only about 5 measures there. I wrote *if* as a guess because I don't know. In those cases where an F# was previously used, we often see a courtesy natural sign later. It's something know, but I wouldn't know whether it applies here which apparently it doesn't.If there is something to be understood in the music that was posted then I would have appreciated knowing it, because I am also a student, and am also learning. So is there something?