In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.
For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ1{\displaystyle {\theta _{1}}} and angle of refraction θ2{\displaystyle {\theta _{2}}} is equal to the ratio of phase velocities v1v2{\textstyle {\frac {v_{1}}{v_{2}}}} in the two media, or equivalently, to the refractive indices n2n1{\textstyle {\frac {n_{2}}{n_{1}}}} of the two media:
sinθ1sinθ2=v1v2=n2n1{\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light, and thus the angle of the refraction also varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.
Hi!
I am dealing with the propagation of electromagnetic emissions through the atmosphere. To quickly outline:
Imagine some charge distribution flying at relativistic speeds and inducing a four-potential A. We define some retarded time at which the charges are at some positions, and calculate...