Journal for Geometry and Graphics 15 (2011), No. 2, 181--193
Copyright Heldermann Verlag 2011
Light Ray Trajectories and Projective Correspondences
Michael Manevich
Dept. of Industrial Engineering and Management, Ariel University Center of Samaria, Ariel 40700, Israel
michael.manevich@gmail.com
Elizabeth Itskovich
Dept. of Industrial Engineering and Management, Ariel University Center of Samaria, Ariel 40700, Israel
elizabeti@ariel.ac.il
This paper considers trajectories of light rays from the position of projective geometry. On the basis of the well-known Law of Reflection the trajectory of a light ray between two intersecting planes is examined. A process of construction leads to a spatial polygon made up from repeatedly reflected rays. It demonstrates that there are projective fields of points involved. We examine the construction of trajectory of a light ray in a diamond. The process of light reflection creates a collineation between two diamond facets. Double points of this collineation indicate the presence of closed light contours inside the diamond. A computer program, developed by the authors, enables users to compare various forms of diamonds and search for the best with respect to light reflection properties.
Keywords: Reflected and refracted rays, collineation, double points, graphical interface.
MSC: 51N05
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