Theoretical solution for light transmission of a bended hollow light guide

This paper presents the theoretical derivation of the model with its graphical representation and coordinate system respecting backward ray-tracing bend distortions. To imagine the resulting illuminance on the horizontal plane element in the interior, the virtual ray (i.e. luminance in an elementary solid angle) has to pass the ceiling diffuser interface, the inner mirror like tube with a bend, through a roof cupola attachment to the element of the sky and sun light source. Due to this complexity and the lengthy derivation and explanations more practical applications will be published later in a separate contribution.