Why does red light travels faster than violet in a transparent medium?

Actually, red light does not travel faster than violet light in a transparent medium. In a vacuum, all colors of light, including red and violet, travel at the same speed, which is the speed of light, approximately 299,792 kilometers per second (or about 186,282 miles per second).

However, when light passes through a transparent medium, such as glass or water, its speed changes. This phenomenon is known as the "index of refraction." The index of refraction is different for each color of light, meaning that each color experiences a different speed when passing through the medium. This difference in speed causes the light to bend, which is known as refraction.

In most transparent media, violet light has a slightly higher index of refraction than red light. As a result, violet light slows down more compared to red light when passing through the medium. The exact values depend on the specific material and its properties.

To summarize, it's not that red light travels faster than violet light in a transparent medium, but rather that violet light slows down more than red light due to differences in the index of refraction for each color.