Question

How is the refractive index of a material related to the velocity of light in vacuum or air and the velocity of light in a given medium?

Answer 1

The bending of the ray of light on passing from one medium to another is called refraction. Suppose $i$ is the angle of incidence in medium 1 and $r$ is the angle of refraction in medium 2, then $\left( {\dfrac{{\sin i}}{{\sin r}}} \right)$is called as the refractive index medium 2 with respect two medium 1. It is also defined as the ratio of the velocity of light in the medium of incidence to that in the medium of refraction.

Formula Used:
The refractive index is given by:
$\mu _2^1 = \dfrac{{{v_1}}}{{{v_2}}}$
where, ${v_1}$ is the velocity of light in the medium of incidence (1) and ${v_2}$ is the velocity of light in the medium of refraction (2).
The absolute refractive index is given by:
$\mu = \dfrac{{\sin i}}{{\sin r}} = \dfrac{c}{v}$
where, $i$ is the angle of incidence in vacuum or air, $r$ is the angle of refraction in the medium, $c$ is the velocity of light in vacuum and $v$ is the velocity of light in the medium.

Complete step by step answer:
The angle between the incident ray and the normal is called the angle of incidence. It is denoted by $i$. On the other hand, the angle between the refracted ray and the normal is called the angle of refraction. It is denoted by $r$. While going from denser to rarer medium, the refracted ray bends away from the normal.

The refractive index is defined as $\left( {\dfrac{{\sin i}}{{\sin r}}} \right)$. It is also defined as the ratio of the velocity of light in the medium of incidence to that in the medium of refraction. For example, if ${v_1}$be the velocity of light in the medium of incidence (1) and ${v_2}$ be the velocity of light in the medium of refraction (2), then the refractive index is $\mu _2^1 = \dfrac{{{v_1}}}{{{v_2}}}$.
The refractive index of the medium when the light is incident from vacuum is called absolute refractive index. It is denoted by $\mu$. Thus,
$\mu = \dfrac{{\sin i}}{{\sin r}} = \dfrac{c}{v}$

Note: Absolute refractive index of vacuum is 1 and that of air is very near to 1. In order for the refraction to take place, the incident ray, the refracted ray and the normal ray should lie in the same plane. Also, the ratio $\left( {\dfrac{{\sin i}}{{\sin r}}} \right)$should be a constant. The refractive index depends on the nature of the media of incidence and refraction. It also decreases with increase in temperature.