title: The generalized Prentice equation and the matrix equation for lens thickness solved simultaneously for dioptric power.
abstract: This paper solves the problem of finding the power of a lens which has given prismatic effect and thickness at a given point. Depending on the conditions there may be no solution or an infinity of solutions. An equation for all the solutions (when they exist) is derived. The paper makes use of matrix results that are new and that are likely to have more general application in ophthalmic optics and vision science. In particular the matrix Sp of Fang and Xu is introduced.
authors.affiliation: Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa.
authors.forename: W F
authors.initials: WF
authors.lastname: Harris
mesh_terms: D006801:Humans; D008433:Mathematics; D055095:Optics and Photonics