Proper convex function Proper convex function In mathematical analysis (in particular convex analysis) and optimization, a proper convex function is a convex function "f" taking values in the extended real number line such that for at least one "x" and for every "x". That is, a convex function is "proper" if its effective domain is nonempty and it never attains formula_3. Convex functions that are not proper are called "improper convex functions". A "proper concave function" is any function "g" such that formula_4 is a proper convex function. For every proper convex function "f" on R there exist some "b" in R and
Lens (optics) real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, "S" then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a "real image" on the retina.