Adding Curvature

Consider the diagram below. The wavefronts from the distant object are parallel and straight. They have no curvature.

When they have passed through the lens they have positive curvature. The lens has added curvature. The more powerful the lens the more curvature it adds.

What would this diagram look like if the wavefronts were from an object which wasn't distant?

Would they still be straight lines?  What would they look like if the lens added the same amount of curvature?

Would they still converge at the focus?

We can imagine that the wavefronts have negative curvature before they go through the lens. The lens adds a certain amount of positive curvature so that they have positive curvature when they emerge but not as much as when they had zero to begin with.

We could write

Curvature after    =    Curvature before    +    Curvature added by the lens

Write this statement out and write the lens equation underneath it. Do you see any similarities?