Originally Posted by Steve Smith
Steve, you're right when the image is in good focus. Out of focus, different result. It's easy enough to explain the general principle.
Imagine a plane through the center of the lens (as in a cutaway showing the lens construction). Imagine pointing the lens directly toward a distant, small subject, such as a star (imagine something larger if that helps). We know that this subject illuminates the entire front of the lens, BUT... consider only the light on one side of our plane - that is, on one half of the lens. As this light converges to form an image, all light is coming from one side of the imaginary plane. As the light passes the ideal focus position, it crosses to the other side of the imaginary plane.
Now repeat this process from the OPPOSITE side of the lens. This light wants to also pass through the focus point and diverge on its opposite side of the imaginary plane. Thus, a double image, but only when out of focus.
I don't consider this as very useful for focusing an enlarger, but a lot of experienced photogs would probably bite on it as a barroom bet.