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One way to understand the refraction of light other than Huygens–Fresnel principle is by Ewald–Oseen extinction theorem, which states that light scatters only in forward direction with a slower velocity. And then we can use Fermat's law to derive Snell's law. However, microscopically, Ewald-Oseen theorem failed to explain why light should change direction inside medium, where does this failure comes from?

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