Which colour of light travels fastest in any medium except air?

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Violet

Red

Blue

Green

answer is B.

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Detailed Solution

Concept: The refractive index of a material is roughly inversely proportional to the square of the incident light's wavelength,

μ \propto \frac{1}{λ^{2}}

, therefore it changes with wavelength. The velocity is also inversely proportional to the refractive index, or ,

μ \propto \frac{1}{ν}

. We can therefore achieve the desired outcome by combining these two relations and wavelengths of various colours.
Refractive index and difference between the absolute and relative refractive index
In a vacuum, light moves at the same velocity or speed regardless of colour.
However, when this multicoloured light enters a medium from the vacuum or when it moves from one medium to another that is not the vacuum, its wavelength changes but its frequencies do not since the frequency of all light is a feature of the light source that is generating it.
A medium's refractive index varies with the wavelength of light incident on it, and as can be seen in the expression below, it is roughly proportional to the inverse of the square of the incident light's wavelength. This explains why, as the wavelength changes, the incident light's velocity also changes. In a vacuum, all electromagnetic waves travel at the same speed, or c, as light. It follows that all light will move at the speed of light, naturally in a vacuum, regardless of its colour.
Unless the light is in a specific medium, like a prism, in which case it depends on the light's refractive index. The relationship between the refractive index and light wavelength is inverse. The visible spectrum's longest wavelength is seen in the colour red. Violet, on the other hand, has the least.
Now,Refractive index is the product of vacuum and medium speeds.Red has a smaller refractive index because its wavelength is longer.Accordingly, violet has the slowest speed and red the fastest in the visible range.
Hence, option 2 is correct.

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