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Home Optics Refraction and Images Derivation of Snell's law  
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Derivation of Snell's law
However intuitively appealing the mechanical model may be, light is a wave, and we should be using wave models to describe refraction. In fact Snell's law can be derived quite simply from wave concepts. In figure (b), trigonometry gives
Eliminating h by dividing the equations, we find
The frequencies of the two waves must be equal or else they would get out of step, so by v=fλ we know that their wavelengths are proportional to their velocities. Combining λ v with v 1/n gives λ 1/n, so we find
which is one form of Snell's law.


Home Optics Refraction and Images Derivation of Snell's law 