Under what conditions would the lateral magnification (m=-i/o) for lenses and mirrors become infinite? Is there any practical significance to such condition?

Magnification of a lens or mirror is the ratio of projected image distance to object distance. Simply put, how much closer does the object appear as a result of the features of the lens or mirror? The object may seem larger or it may seem smaller as a result of it’s projection through a lens or mirror. Take for instance, positive magnification:

If the virtual image appears further than the real object, there will be negative magnification:

The formula for magnification is the following:

The question then is, how can there be an infinite ratio of image size to object size? Consider the equation for focal length:

For magnification to be infinite, the image distance should be infinite, in which case the object distance is equal to the focal length:

In this case, the magnification is infinite:

The meaning of this case is that the object appears as if it were coming from a distance of infinity, or very far away and is not visible. A negative magnification means that the image is upside-down.