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A lens that loses focus during zooming is more properly called a varifocal lens.
It is a varifocal lens.
Many so-called "zoom" lenses, particularly in the case of fixed lens cameras, are actually varifocal lenses.
Varifocal lens By system:
The Kilfitt 36-82 mm/2.8 Zoomar introduced in 1959 was the first varifocal lens in regular production for still 35mm photography.
It becomes necessary to wear glasses just for reading and those who already wear glasses or contact lenses may need to wear bifocal or varifocal lenses.
Progressive or varifocal lenses provide a smooth transition from distance correction to near correction, eliminating segment lines and allowing clear vision at all distances, including intermediate (roughly arms' length).
The progressive addition lens (PAL, also commonly called a progressive or varifocal lens) eliminates the line in bi/tri-focals and is very complex in its profile.
Lenses of this kind are now called varifocal lenses, since when the focal length is changed, the position of the focal plane also moves, requiring refocusing of the lens after each change.
Different lenses have different glazing restrictions, lens material availabilities, maximum and minimum fitting heights, prescription ranges and as such the variation in quality between higher and lower end varifocal lenses is considerable.
Since it is harder to construct a lens that does not change focus with the same image quality as one that does, the latter applications often have lenses that require refocusing once the focal length has changed (and thus strictly speaking are varifocal lenses, not zoom lenses).