This post will cover the Relationships among Speed, RI, Refraction Angle & Deviation Angle of Light of different colors. Light of all colors travels at the same speed in the vacuum. But in the other transparent medium, light rays of different colors are found to travel at different speeds because of their different wavelengths.
Let’s take an example of a glass prism. Here, lights of different colors (and different wavelengths) are found to have different speeds.
As lights of different colors have different speeds within the glass prism, therefore they have different values of refractive index(RI) in glass medium as well.
RI (µ) for a specific colored light is inverse proportional to the speed of that colored light in that medium.
[The RI formula here shows this relationship: µ = c / V, where c is the speed of light in vacuum and which is constant.] See the list of RI formula here
Now, consider the violet ray of light which has the least speed among all VIBGYOR colors.
A lower speed means a higher refractive index (see the above formula). Now higher refractive index denotes higher refraction or bending from the direction of the incident ray of light. In other words, refraction or bending of light is directly proportional to the refractive index.
Now as the RI gets larger, making the refraction more, this means a bigger deviation from the direction of the incident ray. So bigger RI means a bigger deviation angle.
Now as the refracted ray is deviated by a bigger deviation angle, this means the refracted ray gets closer to the normal (perpendicular line on the refracting surface passing through the point of incidence). This means the refraction angle gets smaller.
So in a nutshell:
Lower speed of a colored light => bigger RI => more bending or refraction =>bigger deviation and bigger deviation angle => smaller refraction angle (example Violet colored light)
Higher speed of a colored light => smaller RI => less bending or refraction =>smaller deviation and smaller deviation angle => bigger refraction angle (example red colored light)
Out of the 7 component colors of white light (that got dispersed inside the prism) the speed of violet is the least. Hence violet has the highest refractive index (RI) among all the 7 colors. Violet having the highest refractive index refracts the most, making its deviation angle the largest among the devation angles made by all 7 colors. Hence violet devaites the most from the direction of the incident ray and gets closest to the base of the prism. This is the reason why violet is at the bottom most position of the spectrum.
Read in details : Why violet is at the bottom of a spectrum