A lens designed for photographing a close distance is called a macro lens.
In the macro lens, the magnification can be changed continuously, and the focal length is constant (unchanged) is called macro zoom lens.
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Though the magnification can be changed continuously, the one whose focal length changes will not be strictly a zoom lens.
Sometimes it is called a variable magnification lens distinguished from a zoom lens.
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If you do not change the magnification frequently and want to reduce the price, you should you variable magnification lens. If you change the magnification frequently, a macro zoom lens is recommended.
