>It seems that if you are standing at a certain spot and want to fill the
>frame with the subject, you'd use the zoom feature to do so.  But, is the
>perspective the same as if you used a shorter focal length prime lens and
>moved closer to the subject, assuming that in both cases the subject fills
>the frame to the same degree.

No. Perspective is a function of distance alone. Moving your position with a 
prime lens changes the perspective. Zooming from a fixed position leaves the 
perspective the same and just changes the field of view. 

>Zooms (from my limited experience) seem to have more distortion at the
>wider and longer ends of their focal range compared to primes of a similar
>focal length.  Is that a generally fair statement?

Yes. But that doesn't mean that it's always significant. 

Godfrey

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