Presume that you are asked to find the image position in a problem involving a lens. You are specified the object position and you are told that the lens is a concave lens whose focal point is 12 cm from the plane of the lens. What value must you use for the focal length f of the lens?
Answer:
This is simply a human-established convention. The focal length of the concave (diverging) lens is the negative of the distance from the plane of the lens to the focal point.
If we were discussion about a convex (converging) lens the algebraic sign of the focal length would be positive.