I am trying to figure out what focal length lens I would need to get a specific object to completely fill the image from a camera. Assuming I have two RAW files from the same camera body, shot from the same position, is there a way to create a ratio or equation that would help map the necessary focal length to fill the frame with a given object, such that I could then say "that street light at 100mm is 50x50 pixels, so if I change to an 800mm lens, the ratio is y, so that object is now 200x200 pixels."
Furthermore, once that ratio is calculated, will it always apply to all lenses on that body, or would the ratio change based on the lens? For instance, if I have a 70-200 zoom lens, would changing to a 100-500 yield the same equation or does individual lens optics play a part in the calculation?
I'm considering investing in a longer lens to try out wildlife/birding photography but I'm trying to wrap my head around "800mm would make distant-object-x 'this big' in the frame." I'm trying to figure out whether mathematics can be used to help answer that question definitively.