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Why make it complicated? The simple explanation is that, from Maxwell's equations, c = 1/sqrt(em) where e and m are the permittivity and permeability of the medium.
Transparency is the term given to specific materials such as: plastic, crystal and glass, which allow the wavelengths of visible light to pass straight through them without being captured or scattered. What is surprising about visible light, is that despite being able to pass straight through these media unscathed, it is slowed down throughout its passage, by apparently undergoing deceleration upon entry and acceleration upon exit. Diamond, for example, slows down the passage of visible photons by as much as 50%.