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Red light and violet light travel at the same speed in a vacuum, however, they travel at different speeds relative to each other when traveling through any medium other than a vacuum.

In most media, violet light has a higher index of refraction (usually denoted with the letter n) than red light. The higher the index of refraction, the slower the light goes compared to its speed in a vacuum. This relationship is governed by the following equation: v = c/n where v is the speed of light in a particular medium, n is the index of refraction of light in that medium, and c is the speed of light in a vacuum. Since red light has a smaller n than violet light in most media, red light travels faster than violet light in most media.

The index of refraction is determined by solving Maxwell's equations for a particular frequency and a particular medium using specific boundary conditions.

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