So it seems like there is a pocket of space/light that passes through the lens and is properly transferred/pictured. I assume this is the region of clarity and the outside is blurry. I wonder if any of these properties apply to divergent lenses.
The right shaded represents the range of images whose circles of confusion have a diameter less than C. The two equations on top right gives the boundary conditions for the depth of focus. Solving them with thin lens equation, we get the depth of the field.