Final answer:
The expressions for average powers in the context of oblique incidence with parallel polarization involve analyzing the interaction of the electric field component of an EM wave with a medium, using the small-angle approximation of Snell's law and Malus's law for calculating transmitted intensity.
Step-by-step explanation:
The question pertains to the field of physics, specifically the topic of light polarization and Snell's law in the context of oblique incidence with parallel polarization. To address the question about expressions for average powers transmitted and reflected (P\u00b9\u1d63\u1d52\u2083\u2082, P\u00b9\u1d63\u1d52\u2083\u2082 r, and P\u00b9\u1d63\u1d52\u2083\u2082 t), one must consider how the electric field component of an electromagnetic wave, which is parallel to the incidence plane, interacts with a medium interface.
In the small-angle approximation, where sin \u2248 \u03b8, Snell's law simplifies to n1\u03b81 \u2248 n2\u03b82. This approximation facilitates the analysis of the wave's behavior when it interacts with a different medium. According to Malus's law, only the component of the electromagnetic wave parallel to the filter's axis passes through, and the transmitted intensity I is related to the incident intensity Io by I = Io cos2 \u03b8. While the specific expressions for P\u00b9\u1d63\u1d52\u2083\u2082, P\u00b9\u1d63\u1d52\u2083\u2082 r, and P\u00b9\u1d63\u1d52\u2083\u2082 t are not provided, these principles provide the framework for calculating them.