Question

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

Answer 1

Hint: In this question, we know that the refractive index of a medium is approximately proportional to the inverse of the square of the wavelength of the incident light that is $\mu \propto \dfrac{1}{{{\lambda ^2}}}$, therefore, refractive index changes with wavelength and the velocity in turns is inversely proportional to the refractive index that is $\mu \propto \dfrac{1}{v}$ . Therefore using these two relations and wavelengths of different colour we can get the required result.

Complete step-by-step solution -
Light of different colors travels in a vacuum with the same velocity or speed.
But when these light with different colors enters into a medium from the vacuum or when it travels from one medium to another medium other than vacuum their wavelength changes but their frequencies remain unchanged because the frequency of any light is the property of the light source producing it.
So when the wavelength changes its velocity also changes it is because the refractive index of a medium varies with the wavelength of light incident on it that is the refractive index of a medium is approximately proportional to the inverse of the square of the wavelength of the incident light as can been seen in the below expression.
 $\mu \propto \dfrac{1}{{{\lambda ^2}}}$ ------------ (1)
Now we know that the wavelength of violet light is smaller than that is around 380nm-450nm and the wavelength of red light is the largest that is around 620nm-750nm. So using the relation (1) we get
${\lambda _{red}} > {\lambda _{violet}}$
${\mu _{red}} < {\mu _{violet}}$
The speed of light in glass is not independent of the colour of light it is because the refractive index of violet colour is more than the refractive index of red colour.
Let us assume Absolute refractive index of red colour be ${\mu _{red}}$
The absolute refractive index of violet colour be ${\mu _{violet}}$
Now we know \[{\mu _{red}} < {\mu _{violet}}\]
And as $\mu \propto \dfrac{1}{v}$
Therefore we will get ${v_{red}} > {v_{violet}}$
That is why the velocity of red light fastest.

Note: For these types of questions we need to know about the refractive index and understand the difference between the absolute and relative refractive index. We also need to know the relation between the velocity, refractive index, and wavelength and how they differ for different colors.