Approximations of nonlinear phenomena arising in angular deviations of light rays that emerge from prisms

Monochromatic light rays incident from some directions on a glass prism emerge from the prism with their direction changed. For many thick prisms, emerging light rays are obscured at a boundary. The purpose of this paper is to show that particular light ray deviations can be approximated by polynomials of varying degree over a domain of incident angles. The angles of deviation depend on the apex angle, the direction of incidence with respect to the prism, and the material of the prism. For a prism in air, the incident direction is allowed to vary for a chosen range of apex angles. For each apex angle value and each incident direction, the corresponding ray deviation values are calculated. The theoretical equations for the extremes of angular deviation are nonlinear and awkward to use. Because of their ease of application and goodness of fit, polynomials of varying degree and nature are chosen to approximate these nonlinear equations. Graphical comparisons are made between these approximating polynomial equations and the corresponding exact nonlinear extrema of angular deviation equations. We show that these cumbersome nonlinear equations can very confidently be replaced by their much simpler specific polynomial least-squares approximating equations. The most accurate and easily computed of these approximating equations can then more readily be used in further computations.