# PlanetPhysics/Snell's Law

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Snell's law describes the relationship between an incident ray of light and that of the refracted ray of light at the boundary of two uniform materials. When light goes from one medium to another, Snell's law says that the ratio of the sines of the angles between the normal to the interface and the rays in the two media equals the ratio of the speeds in the two media

${\displaystyle {\frac {\sin \phi _{1}}{\sin \phi _{2}}}={\frac {s_{1}}{s_{2}}}}$

The ratio of the speeds of light in any 3 media is called the index of refraction of the second medium relative to the first

${\displaystyle n_{2,1}={\frac {s_{1}}{s_{2}}}}$

The ratio of the speeds of light in a vacuum to the speed in a given medium is called the absolute index of refraction of the medium. If ${\displaystyle s}$ is the speed of light in a vacuum and ${\displaystyle s_{1}}$ and ${\displaystyle s_{2}}$ are the speed of light in the two media, then the absolute indexes of refraction for the two media are

${\displaystyle n_{1}={\frac {s}{s_{1}}}\,\,\,\,\,\,\,\,n_{2}={\frac {s}{s_{2}}}}$

Combining equations (2) and (3), Snell's law can be written in terms of the absolute indexes of refraction

${\displaystyle n_{1}\sin \phi _{1}=n_{2}\sin \phi _{2}}$

\includegraphics[scale=1]{SnellsLaw2.eps}

{\mathbf Figure 1:} Snell's law

## References

1. Ferry, Ervin S., A Handbook of Physics Measurements . Vol 1. Stanhope Press, Boston, 1918.

This entry is a derivative of the Public domain work [1]