FresnelBeziehungen

Fresnel relations are a set of equations that describe the behavior of light when it encounters an interface between two different optical media. These relations quantify the amount of light that is reflected and transmitted at the interface, and how the polarization of the light is affected. They were developed by Augustin-Jean Fresnel in the early 19th century.

The Fresnel relations depend on several factors: the angle of incidence, the refractive indices of the two media, and the polarization of the incident light. Light can be polarized in two principal directions relative to the plane of incidence: parallel (p-polarization) and perpendicular (s-polarization). The equations provide separate expressions for these two polarization states.

For the s-polarization (electric field perpendicular to the plane of incidence), the reflection coefficient (r_s) and transmission coefficient (t_s) are given by formulas involving the sine of the angle of incidence and the sine of the angle of refraction, related by Snell's law. Similarly, for the p-polarization (electric field parallel to the plane of incidence), the reflection coefficient (r_p) and transmission coefficient (t_p) are derived.

The coefficients represent the amplitude ratios of the reflected and transmitted waves to the incident wave. The intensity of the reflected and transmitted light is proportional to the square of these amplitude coefficients. The Fresnel relations show that at certain angles, such as the Brewster angle for p-polarized light, the reflection can be zero, meaning all incident light is transmitted. Conversely, for s-polarized light, reflection is generally non-zero except at normal incidence where the reflection is minimal. These relationships are fundamental to understanding optical phenomena like glare, the colors seen in thin films, and the design of optical instruments.