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A ray that is perpendicular to the plane of the filter will be undeviated, and this corresponds to zero displacement, and hence zero CA caused by the filter.
The displacement does indeed only happen for rays that are not perpendicular.
Correct. That's the theory. "A ray that is perpendicular to the plane of the filter", however, is an infinitisimal small part of the total of rays hitting that filter. From all directions. Hence the non-occurrence of aberrations for perpendicular rays is insignificant for all real life intents and purposes.
UV filters (a.k.a. haze filters) are useful when there is excess UV light to be filtered.
UV filters (a.k.a. haze filters) are useless when there is NO excess UV light to be filtered!
Worse: they compromise image quality unneccessarily (increased flare, focal softness, chromatic aberration).
So when is there excess UV light that needs filtering? That is 1) at altitude (say, over 3,000 feet), 2) in the desert or savannah, 3) at the beach, 4) at sea, or 5) in snowscapes.
If you're not in any of these circumstances don't use a UV filter (a.k.a. haze filter), because it won't enhance the image, but instead deteriorate it.