Sony a6000 has a Sony E lens mount and currently there are 58 native lenses available for this mount.
Sony a6000 doesn't have a sensor based image stabilization system but 22 of these lenses already comes with optical image stabilization.
Since Sony a6000 has a APS-C sensor, it has a focal length multiplier of 1.5× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on a6000.
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Sony a6000 Lenses with Image Stabilization
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