Question

What is meant by refractive index?

Answer 1

Hint: Recall the basics of refraction of a light ray. From this information, define the term refractive index of a medium. Define the refractive index of a medium in terms of angle of incidence and angle of refraction and speed of light in vacuum and a medium. Hence, give the mathematical expression for the refractive index of a medium in terms of angle of incidence and refraction and speed of light in vacuum and a medium.

Complete answer:
When a ray of light passes from one medium to the other medium, the path of the ray of light deviates from its original direction. This phenomenon of deviation of the path of light is known as refraction of light. The extent of refraction of light depends on the term named refractive index of the medium.

The refractive index \[^1{\mu _2}\] of the second medium with respect to the first medium is defined as the ratio of the speed of the light in the first medium to the speed of light in the second medium. From the above definition, we can write the mathematical expression for refractive index as
\[^1{\mu _2} = \dfrac{{{v_1}}}{{{v_2}}}\]
Here, \[{v_1}\] is the speed of light in the first medium and \[{v_2}\] is the speed of light in the second medium.

We know that in general the refractive index \[\mu \] of the medium is given by the speed \[c\] of light in vacuum and speed \[v\] of the light in a medium.
\[\mu = \dfrac{c}{v}\]
Also, we know that the formula for refractive index of a medium according to Snell’s law is given by
\[\mu = \dfrac{{\sin i}}{{\sin r}}\]
Here, \[i\] is the angle of incidence of the light and \[r\] is the angle of refraction of the light.

Note:The students should remember that the refractive index of the medium is the ratio of speed of light in vacuum to speed of light in a medium only when we are determining the refractive index of a medium with respect to the vacuum as the speed of light in the first medium is equal to the speed of light in the vacuum. Otherwise, this equation will not be applicable to determine the refractive index of the medium.