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 object to be formed at the near point, labelled D, 25 cm from the eyes. We assume the distance from the eyes to the lens is zero, so we can take the image to be distance D from the lens.
Now use the thin lens equation
to give
When the image is formed at the near point,