# Can a ratio/function be created to calculate focal length vs size-in-frame if I have two focal length shots from the same sensor and position?

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.

• When I go on bird walks the most common rig I see is a 100-400 zoom on an APS-C body, giving an effective focal length of 640mm. I have read about 150-600 zooms from Sigma and Tamron but have not seen them. I do a lot of bird photography and would not use anything less than 600mm effective. Most of the time I use a Nikon P900 with its 2000mm effective focal length. The whopping zoom range means the lens is not as crisp as the shorter zooms, but with practice one can find the bird and hand hold it. Commented Feb 17, 2021 at 16:12

This said, there are limits to the usability of long lenses. A 800mm lens that you can carry around with have a rather small aperture (f/5.6 at best or even f/8) and in anything but very bright conditions you won't be able to use sufficiently short exposures to compensate for the increased sensitivity to camera shake. In addition such lenses are expensive (if good enough) and difficult to master (try shooting birds in flight...). Another limit is... your eyesight: you can't shoot a bird you didn't spot first, so it has to be close enough for you to see it. Your best zoom is proper behavior/technique and proper attire, a $20 ghillie suit may be a better investment than a$2000 lens.