XLVI. Note on elementary nomenclature in Geometrical Optics

Matrix Methods in Geometrical Optics

As well as the geometrical methods used for solving lens problems, and locating the size and position of images in optical systems, there is an alternate, perhaps more versatile, method involving matrix manipulation. Many of you will be familiar with the use of simple 2x2 matrices. Firstly, however, before I consider the use of matrices in optics, I will review the matrix solution of two simult...

Multiphase Computations in Geometrical Optics

In this work we propose a new set of partial diierential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases. The traditional geometrical optics pair of equations suuer from the fact that the class of physically relevant solutions is limited. In particular, it does not include solutions with multipl...

Elementary Ophthalmic Optics

Elementary Ophthalmic Optics

out that we are convinced every student of refraction should make himself acquainted with Mr Parsons' work. It is exceedingly well arranged and clearly expressed and the mathematical problems are stated with such lucidity that no one with a fair knowledge of mathematics can fail to follow them I he work may be said to stand midway between Hartridges Refraction and Donder s big work while improv...

A Note on Elementary Derivations

Let R be a UFD containing a field of characteristic 0, and Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5] that if D is an R-elementary monomial derivation of B3 such that kerD is a finitely generated R-algebra then the generators of kerD can be chosen to be linear in the Yi’s. In this paper, we prove that this does not hold for B4. We also investigate R-elementary...