Question

How is the refractive index of a medium related to the speed of light? Obtain an expression for the refractive index of a medium with respect to another in terms of speed of light in these two media?

Answer 1

Step 1: Refractive index:

1. Refractive index of a medium is defined as the ratio of the velocity of light in air and the velocity of light in that medium.
2. Refractive index, $\mu =\frac{c}{v}$, c is the velocity of light in air and v is the velocity of light in the medium.

Step 2: Finding the relative refractive index:

Let $v_1$ and $v_2$ are the velocities of light of mediums 1 and 2 respectively. And ${\mu }_1$ and ${\mu }_2$ are their refractive indices.

Now, the refractive index of the first medium, ${\mu }_1=\frac{c}{v_1}$ and the refractive index of the second medium, ${\mu }_2=\frac{c}{v_2}$, where c is the velocity of light in air.

The refractive of the second medium with respect to the first is ${}_1{\mu }_2$,

${}_1{\mu }_2=\frac{{\mu }_2}{{\mu }_1}=\frac{{\displaystyle \frac{c}{v_2}}}{{\displaystyle \frac{c}{v_1}}}=\frac{v_1}{v_2}$.

⇒${}_1{\mu }_2=\frac{v_1}{v_2}.$

Therefore, the refractive index of the second medium with respect to the first is $\frac{v_1}{v_2}$.