Angle of refraction: Encyclopedia II - Angle of refraction - Derivation and Meaning of the Angle of Refraction

Angle of refraction - Derivation and Meaning of the Angle of Refraction

There are several ways to derive Snell's Law, and therefore the Angle of Refraction. The first way it was discovered was by an application of Fermat's principle which states that a light wave must take a path that is an extremum in time subject to the constraints present. Normally this is translated into "Light will always take the quickest path it can." From this principle, and using a bit of differential calculus, Snell’s Law can be derived thus leading to the Angle of Refraction. If one looks into the meaning of Fermat’s principle, other uses can be seen for the formula as well. For instance, if a truck needs to drive across a parking lot and a grassy field and traverse in a direction parallel to the place the asphalt and the grass meets, Snell’s law can be used to find at what angle you should drive on both the asphalt and the grass exchanging the refractive indices with the speeds the truck can drive on the two surfaces. Using Snell’s Law will ensure the quickest path possible.

There are several other ways to derive Snell’s Law. One of the easiest involves an application of the general boundary conditions of Maxwell equations for electromagnetic radiation. It can also be done geometrically by applying Fermat’s principle through a prism.

The result of this is that the angle a wave is heading will decrease according to the normal if it passes from into a denser medium from a less dense, and will increase if it passes into a less dense medium from a denser one. If a wave passes into and then out of a material, it will leave with the same angle it entered with.

Adapted from the Wikipedia article "Derivation and Meaning of the Angle of Refraction", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki