Snell's law

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A ray of light hits a glass prism and is refracted

Snell's law is the scientific law of the refraction of light or other waves. In optical science, Snell's law is about the relationship between the angles of incoming and outgoing light to the refractive indices of the mediums. The law states that when light passes through different materials (for example from air to glass) the ratio of sines of the incidence (incoming) angle and the refraction (outgoing) angle does not change:

\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}

with each \theta as the angle measured from the normal of the boundary, v as the velocity of light in the respective medium (SI units are meters per second, or m/s) and n as the refractive index (which has no units) of the medium. The index of refraction of a vacuum is 1 and the velocity of light in a vacuum is c. When a wave passes the material where the index of refraction is n, the velocity of the wave becomes \frac{c}{n}.

Snell's law can be proved by Fermat's principle. Fermat's principle states that light travels along the path which takes the least time. We can understand Fermat's principle through an example in which when we run to the water from the sands to save a drowning person. In this case, our speeds change as we move from sand to water.