Apparent and actual radius (Optics)

[Healthycola]

I know the radius of a circle. I'm taking pictures of the circle as I bring it closer to the camera. Obviously the radius is getting larger. I want to know what the relationship is to find this out? I know the distance from the camera that the circle is at all times.

 

[jtbell]

I think the concept you're looking for is linear magnification a.k.a. transverse magnification:

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lensdet.html#c2