Close up of monochromatic aberrations using Snell's law: an undergraduate computational experiment

Abstract

Images formed from light rays refracting a spherical surface are often introduced in textbooks using the paraxial approximation. Incoming rays propagating from the object meeting the surface of a transparent medium at a given point for which the angle is larger than 15° with respect to the normal are not described accurately from the paraxial approximation. Instead of using the paraxial approximation, the fundamental law of refraction (Snell's law) is used in this paper to predict the image location of an object situated at a given distance from a refracting spherical surface. Positions of focal points are also computed for incident rays refracting at various positions along the spherical curvature to illustrate the concept of spherical, comatic and astigmatic aberrations. Computations of aberrations from plano-convex lenses are also presented and proper positioning of lenses in order to reduce aberrations when focusing is also discussed.