The angular magnification
of an optical instrument is defined as the ratio between the angle subtended normally by an object and the angle subtended when using the instrument. The word 'normal' used here depends on the situation.
The largest angle that an object can occupy is when it is placed at the near point:
below.
A simple magnifying glass can increase the angle subtended.
We can arrange for the image to be at infinity by moving the magnifying glass or object until the object is at the focal point.
The angle
The angular magnification