Replacing an arbitrary ‘black box’ ray matrix with a single lens. an optical black box has various optical elements inside it, producing a given real abcd matrix from its input plane to its output plane. we want to replace this black box with a box of physical length l, containing only a single lens of focal length f. can this be done? why? and if so, what total length l, focal length f, and lens location x (within l) will be required?