Well I’m no expert, but this is my understanding.
First off, a teleconverter is a lens adapter that mounts on the camera, has camera glass type optics, and multiplies it’s focal length. A Barlow is an add on eyepiece for a telescope with a simple lens system that multiplies its focal length. A powermate (brand name, not a term?) is like a Barlow but it has extra optical elements which help overcome some of the optical flaws that’s Barlow’s introduce. I guess it’s almost like a teleconverter for a telescope.
So they’re all slightly different implementations of ways to multiply your focal length.
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