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Light propagates through a transparent or translucent solid in roughly the same way as it does through a clear or murky liquid, or a clear or foggy gas, respectively. The difference is the overall rate at which it accomplishes the propagation (which is a matter of electrodynamics), although it's worth mentioning that the photons themselves always move at exactly c, the constant speed of light. To understand the distinction, imagine a game of "hot potato". You hold the potato in your hand for a non-zero amount of time, and that affects the overall propagation rate (the speed of potato in a medium), even if the potato always moves faster than that between two people (the speed of potato in a vacuum).