Wide-field EPs - how do they do it?

Continuing from my question yesterday about widest true field, the answers to which prompted even more questions:

Most importantly, given the the way the calculation for Actual FOV works, I don't understand how "Wide Field" EPs actually give you a wider field. Going by the equation from Televue's website, it's clear that Actual FOV is determined solely by the size of the field stop. How does a Pentax XL/Meade SWA/UWA/Nagler/etc actually give you a wider field than what that equation seems to dictate?

They don't. There are two measurements of "field", TRUE field of view (TFoV) and APPARENT field of view (AFoV). Think of a little circle projected onto the sky that you look at with the naked eye and suppose that what you can see inside that circle is what you can see in the eyepiece. If you've ever seen a Telrad or Rigel Quickfinder this is particularly easy to imagine. The TFoV is the angle your eye sweeps out as you look (without telescope) from one edge of this little circle to the opposite edge along a diameter. The AFoV is the angle your eye sweeps out as you look from one edge of the field in the eyepiece to the opposite edge. Your telescope+eyepiece projects the the TFoV into the AFoV (that's magnification).

All these super- and ultra-wide angle eyepieces are doing differently in one sense is to project the same TFoV into a larger AFoV. In other words, they magnify the same TFoV a little more versus another eyepiece with a smaller AFoV and the same TFoV. For example, the 20mm Tele Vue Plossl and 12mm Nagler Type 4 both have 17.1mm field stops and hence the same true field of view. The 12mm Nagler Type 4 just presents that same view to your eye at a greater magnification. Look from one edge of your computer monitor to the opposite edge. Now move your face 50% closer and repeat. Same TFoV, bigger AFoV. No magic there.
--
Mike