Knowing that, the following scope magnification...
3-15x50mm
...breaks down as...
3-15
Zoom Range (3 to 15x)
x50mm
Lens Size
Therefore, the zoom size of the above example is a range between 3 and 15 times the actual 'picture'. Lens size dictates the overall picture size as well as clarity due to more light entering the lens.
Similarly, the following scope magnification...
1.5-4x20mm
...breaks down as...
1.5-4
Zoom Range (1.5 to 4x)
x20mm
Lens Size
Again, the zoom size of the above example is a range between 1.5 and 4 times the actual 'picture' - considerably smaller than the perious example and maybe perferable when hunting smaller game at closer ranges. The lens size dictates an overall picture of 20mm.