In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics and gemology to find the refractive index of a material.

Refraction of light at the interface between two media of differentrefractive indices, with n₂ > n₁. Since the velocity is lower in the second medium (v₂ <>₁), the angle of refraction θ₂ is less than the angle of incidence θ₁; that is, the ray in the higher-index medium is closer to the normal.

Snell's law is also satisfied in the metamaterials which allow light to be bent "backward" at a negative index, with a negative angle of refraction.

Named after Dutch mathematician Willebrord Snellius, one of its discoverers, Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities in the two media, or equivalent to the opposite ratio of the indices of refraction:

or

Snell's law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves.

Above are taken from http://en.wikipedia.org/wiki/Snell's_law

Summary:

Snell's law gives the relationship between angles of incidence and refraction for a wave impinging on an interface between two media with different indices of refraction. The law follows from the boundary condition that a wave be continuous across a boundary, which requires that the phase of the wave be constant on any given plane, resulting in