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Carl,
The typical development of the paraxial approximation involves approximating
sines and cosines by their first order expansions. This includes not only
the angle which a ray makes with the optical axis, but also the angle which
a ray makes with the normal to the spherical refracting/refracting surface.
This latter angle can be large for a ray parallel to the axis depending on
where it strikes the spherical refracting/reflecting surface.
(Refer to the development in any optics text)
Bob Sciamanda