Why is the angle of deviation different for different colours?

Last updated on April 21st, 2023 at 04:05 pm

This post will cover why the angle of deviation is different for different colours. We will also see how the deviation angle, refraction angle, and refractive index are interrelated and all these again depend on the speed of light rays of different colours.

The angle of deviation is different for different colours – explanations

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 inversely 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 a vacuum and which is constant.] See the list of RI formulas here.

µ = c / V, where c is the speed of light in a vacuum and which is constant

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, the 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: using this formula µ = c / V
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)

Read this Case Study: why is violet at the bottom of a spectrum