The focal ratio determines how much light is gathered when the shutter is open. The sensor size does not matter.
This is because you have to think of the light gathering not as a "total" but as a "per unit area". Obviously if I have a space which is exactly 1" square and another area which is precisely 2" square and they are both equal distance from the same light bulb, the "area" which is 2" square will actually have twice as many photons land on that space. But if we ignore the total space and just pick a unit-area (say we only bother to measure the light falling on a sample piece which is 1 centimeter square in the middle of our 1" or 2" areas) the amount of light falling on those "per unit areas" will be identical (assuming they are located precisely the same distance from the same light bulb when we measure the light.)
Another way to think of this... suppose I have a movie projector and I'm projecting a movie onto a screen which measures 12' tall and 18' wide.
NOW... suppose I remove that 12x18' screen and replace the movie screen with a smaller screen which only measures 6' tall and 9' wide BUT I place that screen at PRECISELY the same distance from the movie projector and I do not touch the projector at all (no adjustments to how much I zoom in, etc. are changed.) The question is... will the image suddenly get dimmer on the small screen?
The answer is, of course, no... much of my projected movie may miss the screen entirely and spill off onto the wall in the background, but the brightness of a projection of an image onto a movie screen that's (let's just use an example) 10' away from the projector is the SAME amount of light that can make it 10' away from the projector... period. I could take a pair of scissors and cut half the movie screen away... and the part of the screen I did NOT cut away would look the same.
The properties of a lens which are significant is that it has some given focal "length" and it also has an aperture opening of some "diameter". I could have a lens which is 100mm long ... but a diameter of 25mm wide. 25mm divides into 100mm exactly four times. So that would be "f/4" as our focal "ratio". (the notion f/___ means focal-ratio with the following number telling you what the ratio of the length divided by diameter works out to be.)
I could then change that 100mm lens out for a 24mm lens... and let's suppose the 24mm lens has an aperture opening which is 6mm wide.
The "problem" with this scenario is that if I sell you a lens by listing out all its dimensions then it might not be obvious to you that the ratio of 100mm ÷ 25mm happens to be the SAME ratio as 24mm ÷ 6mm... even though they are. It turns out the amount of light conveyed through the lens per unit of time will be exactly the same (given the two cameras are in the same location with identical lighting.)
So rather than tell you the focal length and the physical diameter of the aperture opening... it's more useful to a photographer to just know the "focal ratio" (regardless of the actual length & diameter). I can use a light meter to check the available light under the shade of a tree, it might tell me that there's enough light to take a photo at ISO 100 with a 1/100th second exposure IF I set my aperture to f/8 (I'm making this up)... but notice what the light meter does NOT need to know... is the focal length of the lens I'll be using to take the photo. It also doesn't need to know the make, model, or sensor size of the camera I'll be using. This is because f/8 is f/8 is f/8... regardless of what camera you are using.