Linear vs. Angular Magnification?

When an object is placed in front of a suitable mirror it produces an image somewhere.

The height of the image divided by the height of the object is the linear magnification.

The problem is that the image might be close or it might be a long way away.

The APPARENT magnification is quite different.

A hill 30Km away seems small. A toy up close seems large. But Why?

The apparent size comes from the angle that lies between rays from the extremities of the object.

To get angular magnification consider looking at the object with your eyes from some initial condition.

Find the angle between rays from the extremities of the object.( Object angle)

Now apply your lens mirror combination and once more find the angle between these rays.( image angle.)

The angular magnification is image angle/object angle and it in fact is a measure of the apparent magnification as seen by us.

Linear Magnification