Refraction and total internal reflection in a prism with an arbitrary apex angle

Abstract We study the reflection and refraction of a monochromatic ray of light in a normal or rhomboid-shaped prism with an arbitrary apex angle. In particular, we investigate the conditions for the occurrence of the total internal reflection and propagation of light on the second surface of the prism by varying the incidence angle, apex angle, and refractive index of the prism. The regions within the two-dimensional incidence angle – apex angle and incidence angle – refractive index spaces, which correspond to refraction or total internal reflection occurring at the surfaces of the prism, are characterized in detail. Thus, this study facilely obtained solutions to the typical problems of refraction and total internal reflection in a prism.