Refractive index – definition, formula, dependence, List

If you emerge a straight pencil into a glass of water, you can see the part of the pencil inside the water is bent. The pencil does not bend. It appears to be bent because the light bends while passing from one medium to another medium. Now, the question is, why does light bend when it changes medium? This is due to the different refractive indices of different mediums. In this article, we’re going to discuss the refractive index, its definition and formula. On what parameters does the index of refraction depend? A list of refractive index of some popular materials is also provided here.

Contents in this article:

• Definition of refractive index of a material
• Refractive index formula
• Unit of index of refraction
• On what parameters does the refractive index of a material depend?
• List of refractive indices of different materials
• Numerical problems

Definition of refractive index of a material

The refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium. Since the speed of light is greater in vacuum than any other medium, the index of refraction is always greater than unity (1). The refractive index of a medium with respect to the air medium is the absolute refractive index of that medium and the refractive index of a medium with respect to any medium other than air is the relative refractive index of the medium.

Refractive index formula

If v is the speed of light in a medium then the formula for refractive index of that medium is, {\color{Blue} \mu = \frac{c}{v}}……..(1)

Where c is the speed of light in free space or vacuum. Equation-(1) gives the relation between refractive index and speed of light.

Refractive index in terms of the wavelength of light:

The speed of a wave is the product between its wavelength and frequency. Then, speed of light, {\color{Blue} v = \lambda \nu}. After the refraction of light, the frequency of the wave does not change.

Then the refractive index in terms of the wavelength of light is {\color{Blue} \mu = \frac{\lambda_{0}}{\lambda}}……………(2)

Where \lambda_{0} is the wavelength of light in vacuum and \lambda is the wavelength of light in that medium.

Unit of refractive index

As the refractive index is the ratio of two speeds, then it is a unitless physical quantity. So, the refractive index does not have any unit.

On what parameters does the refractive index of a material depend?

The refractive index of a material depends on the following parameters –

• Color or wavelength of the incident light.
• The nature of the medium.
• The density of the medium.

List of refractive index of different materials

Here is the list of refractive indices of different materials like water, air, glass, diamond, Teflon, etc.

Material	Refractive index
Water	1.33
Glass	1.51
Air	1.00
Diamond	2.42
Teflon	1.315
Silicon	3.42 – 3.48
KDP	1.49 – 1.51 (depends on the wavelength of light)
Benzene	1.501
Kerosene	1.39
Lens (human)	1.386 – 1.406

How to find refractive index of a material?

One can find the refractive index of a medium in two ways –

• By knowing the value of the speed of light in that medium and then using the equation-(1).
• By using Snell’s law of refraction of light.

Here is a detailed post on the ways to find refractive index of a material.

Numerical problems and solutions

1. The refractive index of glass is 1.5. what is the speed of light in glass?

Answer: The formula for refractive index of a medium is, {\color{Blue} \mu = \frac{c}{v}}.

Now, speed of light in glass, {\color{Blue} v = \frac{c}{\mu}}

or, {\color{Blue} v = \frac{3\times10^{8}}{1.5}}

or, v = 2×10⁸ m/s. This is the speed of light inside the glass medium.

This is all from this article on index of refraction of a medium. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

Related posts:

1. Snell’s law of refraction of light.
2. Refraction of light