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.

我们研究具有任意顶角的法线或菱形棱镜中单色光的反射和折射。特别地，我们通过改变棱镜的入射角，顶角和折射率来研究在棱镜的第二表面上发生全内反射和光传播的条件。详细描述了二维入射角-顶角和入射角-折射率空间内的区域，这些区域与棱镜表面上发生的折射或全内反射相对应。因此，本研究轻松地解决了棱镜中折射和全内反射的典型问题。