Fresnelyhtälöt

Fresnelyhtälöt, also known as Fresnel equations, are a set of equations that describe the reflection and transmission of light (or other electromagnetic waves) at an interface between two different dielectric media. They were derived by Augustin-Jean Fresnel in the early 19th century. The equations relate the amplitude of the reflected and transmitted waves to the amplitude of the incident wave, and depend on the angle of incidence, the polarization of the light, and the refractive indices of the two media.

There are two main cases for polarization: p-polarization (where the electric field is parallel to the plane of incidence) and s-polarization (where the electric field is perpendicular to the plane of incidence). The Fresnel equations for these two polarizations are different. For s-polarized light, the reflection coefficient is given by r_s = (n1*cos(theta_i) - n2*cos(theta_t)) / (n1*cos(theta_i) + n2*cos(theta_t)), where n1 and n2 are the refractive indices of the first and second medium, respectively, theta_i is the angle of incidence, and theta_t is the angle of transmission. For p-polarized light, the reflection coefficient is r_p = (n2*cos(theta_i) - n1*cos(theta_t)) / (n2*cos(theta_i) + n1*cos(theta_t)). The transmission coefficients are derived similarly.

The Fresnel equations are fundamental in optics and electromagnetism. They are used to calculate phenomena such as the amount of light reflected from a surface, like water or glass, and are crucial for understanding optical instruments, coatings, and the behavior of light in various optical systems. For normal incidence (theta_i = 0), the equations simplify considerably.