I don't believe magnification is a term used to characterize lens.
Suppose we have an...
85 1.8g lens on a d800. The magnification is 1:8.
85 1.8g lens on a d7000 The magnification is also 1:8.
I believe you are referring to an 85mm f/1.8G lens and the f/1.8 does NOT designate the "magnification"; it is the ratio of the focal length over the aperture. An 85mm f/1.8 has an opening at the front of the lens (effectively) that is 85/1.8mm or 47mm. That is the maximum possible opening for light to enter that lens. The greater the opening, the greater the light allowed in. An 85mm f/1.4 lens would have a maximum opening of 85/1.4=61mm. The term magnification is irrelevant and probably is holding you back from an accurate understanding of optical concepts involved with photography.
I don't quite understand the relationship between focal length, DOF and magnification.
You probably won't learn the fundamentals here on this forum. At best, someone will give you a little insight or a different way of thinking about a concept. For DOF fundamentals try this web site:
I understand that we loose a f stop when shoot crop-frame (f1.4 turns into f2)
No this isn't true. The aperture of a given lens remains the same despite the size of the sensor behind it. The "f-stop" is a property of the lens by itself.
and that we multiple the focal length by 1.5 (85mm becomes 127.8mm), but why doesn't the magnification change?
This is true (equivalent focal length get multiplied by 1.5) but a somewhat limited understanding of the concept. The "magnification" DOES increase by 1.5 when we take a given lens off of a D800 and install it on a D7000. The field of view changes by that amount and a good explanation requires some good diagrams (which I can't provide here).
Because it's a ratio? If put the 85 1.8g on a cropped body, I get closer, and doesn't that allow me better magnification? Apparently it doesn't...
Yes, it does. Good luck in your search for answers Try this link below for help: