I'm a beginer photographer and im trying to understand the apperature correctly. Im interested in how it works, but also i want to know what can i expect from the apperateure from any future lens purchases. I've searched far and wide about this, but i have not found quite the answer i was looking for.

So my understanding: Lets say i have a 50mm lens at f/4, that should mean 50/4 so 12.5mm open apperature "hole".

Then lets say i would have a 200mm lens again at f/4, that should mean 200/4 and thats 50 mm "hole".

The 200mm should let more light in because its open much wider, BUT since its longer focal lenght its "croped" more tight, it WONT capture more light than the 50mm because the 50mm can see more of whats in front of it right?

So is it a case that the larger apperature opening on longer focal lenght lenses is countered by the "crop" of said lens? Or do i not understand it correctly?

Now does that mean that both lenses mentioned above at f/4 catch roughly the same amount of light?

So for example, if i can use my 50 mm at f/4 at certain light conditions, could i expect the 200mm at f/4 to act roughly the same exposure wise, at the same light conditions?

Or am i completely wrong about understanding anything about apperature and every lens is just different? I know i can rent lenses and try it, but i would like to understand it so its not all guesswork.