Answer:
A beam of light (implicitly a plane wave) in vacuum or in an isotropic medium propagates in the particular fixed direction specified by its Poynting vector until it encounters the interface with a different medium. The light causes the charges (electrons, atoms, or molecules) in the medium to oscillate and thus emit additional light waves that can travel in any direction (over the sphere of 4π steradians of solid angle). The oscillating particles vibrate at the frequency of the incident light and re-emit energy as light of that frequency (this is the mechanism of light “scattering”). If the emitited light is “out of phase” with the incident light (phase difference ∼= ±π radians), then the two waves interfere destructively and the original beam is attenuated. If the attenuation is nearly complete, the incident light is said to be “absorbed.” Scattered light may interfere constructively with the incident light in certain directions, forming beams that have been reflected and/or transmitted. The constructive interference of the transmitted beam occurs at the angle that satisfies Snell’s law; while that after reflection occurs for θreflected = θincident. The mathematics are based on Maxwell’s equations for the three waves and the continuity conditions that must be satisfied at the boundary. The equations for these three electromagnetic waves are not difficult to derive, though the process is somewhat tedious. The equations determine the properties of light on either side of the interface and lead to the phenomena of:
1. Equal angles of incidence and reflection;
2. Snell’s Law that relates the incident and refracted wave;
3. Relative intensities of the three waves;
4. Relative phases of the three light waves; and
5. States of polarization of the three waves.
Explanation:
