Question

(a) The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times {10^8}$ m/s)
(b) Is the speed of light in glass independent of the colour of light? If not, which of the two colour red and violet travels slower in a glass prism?

Answer 1

Hint: In this question, we will first find the velocity of light in glass by using the expression $v = \dfrac{c}{\mu }$. Then we also know that the speed of light in glass is not independent of the color of light it is because the refractive index of violet color is more than the refractive index of red color and by using $v = \dfrac{c}{\mu }$ we can calculate which color has more velocity.

Step-By-Step answer:
The refractive index of a material is a dimensionless quantity that defines how fast light travels through the material. It is defined as the ratio of the speed of light in a vacuum to the phase velocity of light in the medium.
Let us take $c$ be the velocity of light and $v$ be the phase velocity of light in the glass. Then refractive index can be written as
$\mu = \dfrac{c}{v}$
The absolute refractive index of glass $\mu = 1.5$
The Velocity of light $c = 3 \times {10^8}$ m/s
The Velocity of light in glass $v$ is
$v = \dfrac{c}{\mu }$
$ \Rightarrow v = \dfrac{{3 \times {{10}^8}}}{{1.5}}$
$ \Rightarrow v = 2 \times {10^8}ms$
No, the speed of light in glass is not independent of the colour of light it is because the refractive index of a violet colour is more than the refractive index of a red colour.
Let us assume Absolute refractive index of red color be ${\mu _r}$
The absolute refractive index of violet color be ${\mu _v}$
Now we know \[{\mu _r} < {\mu _v}\]
And as $\mu \propto \dfrac{1}{v}$
Therefore we will get ${v_r} > {v_v}$
That is why the velocity of red light is more than that of the velocity of green light in the glass.

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 and refractive index of how it differs for different colors.