Paper Info
Title
Approximations of nonlinear phenomena arising in angular deviations of light rays that emerge from prisms
Abstract
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.
Year
DOI
Venue
2008
10.1016/j.camwa.2007.03.023
Computers & Mathematics with Applications
Keywords
Field
DocType
varying degree,angular deviation of light rays,apex angle,angular deviation,incident direction,angular deviation equation,transmission prisms in optics,nonlinear phenomenon,cumbersome nonlinear equation,thick prism,incident angle,continuous least-squares approximations,least-squares chebyshev polynomial approximations,corresponding ray deviation value,light ray,corresponding exact nonlinear extremum,least square,goodness of fit,chebyshev polynomial,nonlinear equation,least squares approximation
Monochromatic color,Mathematical optimization,Nonlinear system,Ray,Polynomial,Mathematical analysis,Maxima and minima,Prism,Geometry,Goodness of fit,Mathematics,Computation
Journal
Volume
Issue
ISSN
55
3
Computers and Mathematics with Applications
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Shirley Abelman1184.71
Herven Abelman200.68