A heuristic approach to the lens equation
An experimental approach to obtaining the reciprocal relationships involved in a study of lenses is introduced. Through an analysis of the data obtained for the combination of two lenses of different focal lengths one finds a formula for the combination in terms of the data for individual lenses by arguing by analogy. This procedure then suggests a way to find the relationship between the image distance and object distance of a lens. Graphing the variables and 'ray diagrams' are introduced, to obtain the same relationship. Finally, it is argued that the relationships among variables of other phenomena, which show similar quantitative relationships, may be obtained by analogy.
Physics, Astronomy, and Materials Science
Whitaker, Robert J. "A heuristic approach to the lens equation." Physics Education 46, no. 1 (2011): 97.