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Does the value of speed of light change with medium?

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Yes it does change with the change in medium because different mediums have different optical densities. Some are optically denser(higher refractive index) like oil, diamond etc in which the light travels at a slower speed and bends towards the normal, whereas some other materials can be optically rarer(lower refractive index) like air, water in which light speeds up and bends away from the normal.

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