I got into birding recently and got a pair of 10x42 binoculars and got a camera with a crop ratio of 1.6 and a 100-400mm (focal length) lens.
With binoculars and spotting scopes everything seems easy - you get a magnification number, so it easy to grasp the idea of how close the objects will appear through it. My 10x42 binoculars have 10x magnification - easy.
Now with lenses, it get's much more tricky, I read several SE questions about that and I understand that full frame camera x 400mm will produce similarly magnified image as a camera with 1.6 crop ratio and a 250mm lens (1 x 400 = 1.6 x 250). But I cannot find any formula how to convert that into magnification and compare with my binoculars. And I think I also understand what zoom means - my lens has a zoom of 4 (= 400 / 100), but it is a useless number in this conversation.
So I read in multiple places that a naked human eye is very close to 50mm (one place gives 43mm) camera lens on a full frame camera. So going by that, 400mm lens on a full frame camera would have 8x (= 400/50) magnification and 400mm lens on a 1.6 crop ratio camera, would have 12.8x (= 400/50*1.6) magnification? It this how it works? And either way, what is the fundamental reason, that photographers don't talk about magnification of lenses, but binocular users do?