Refractive Index

  

Understanding Light's Behavior in Different Media

Snell's laws describes how light behaves as it passes from one transparent medium to another. It describes how the speed of light changes as it travels through different media, affecting the bending of light rays and the resulting refraction.

The bending of light when it passes from one transparent medium to another is termed as refraction of light.

The refractive index (RI) of a material is a measure of how much light slows down when it passes through that material compared to its speed in a vacuum. In a vacuum, light travels at its maximum speed, denoted by the speed of light in a vacuum, approximately 3.00× 10⁸ meters per second. It quantifies the bending of light as it enters a different medium.

Relative Refractive Index:

Relative refractive index is a dimensionless ratio. It compares the speed of light in one substance to its speed in another substance.

It's a comparison between the speeds of light in two different materials. It indicates how much slower or faster light travels in one substance compared to another.

n₂₁ (RI of Medium w.r.t. Medium 1)  = Speed of Light in Medium 1/ Speed of Light in medium 2

                                                               = v₁/v₂

Example:

 The Refractive Index of glass w.r.t. water is either denoted by n𝐠𝐰

n𝐠𝐰 = Speed of Light in Water/ Speed of Light in Glass

Problem:

Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 x 10⁸ m s⁻¹

Solution:

Given:

Refractive Index of glass w.r.t. air (n𝐠𝐚) = 1.50

Speed of light in vacuum (V𝐯𝐚𝐜𝐜𝐮𝐦)     = 3 x 10⁸ m s⁻¹

To find speed of glass i.e. V𝐠𝐥𝐚𝐬𝐬

We know, n𝐠𝐚 = V𝐯𝐚𝐜𝐜𝐮𝐦/V𝐠𝐥𝐚𝐬𝐬

            V𝐠𝐥𝐚𝐬𝐬 = V𝐯𝐚𝐜𝐜𝐮𝐦/n𝐠𝐚

                         = 3 x 10⁸ m s⁻¹/1.5

                         = 2 x 10⁸ m s⁻¹

⸫ Speed of Light in glass = 2 x 10⁸ m s⁻¹

Absolute Refractive Index:

When medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium. It is simply represented as n𝐦

n𝐦 (Refractive Index of Medium ) = Speed of Light in Vacccum/ Speed of Light in Medium

                                                             = c/v𝐦

The absolute refractive index of a medium is simply called its refractive index.

Speed of Light in medium v𝐦 = Speed of Light in Vacccum/n𝐦(Refractive Index of Medium)

The higher the refractive index of a material, the less the speed of light in the medium.

The refractive index of diamond is 2.42. What is the meaning of this statement?

The statement "The refractive index of diamond is 2.42" means that when light travels from a vacuum or air into a diamond, it slows down considerably. The refractive index of diamond, which is 2.42, indicates how much the speed of light is reduced or how much the light bends when it enters the diamond compared to its speed in a vacuum.

Mathematically,

𝜇𝐝𝐢𝐚𝐦𝐨𝐧𝐝  = Speed of Light in Vacuum/Speed of Light in Diamond

Speed of Light in Diamond = Speed of Light in Vacuum/𝜇𝐝𝐢𝐚𝐦𝐨𝐧𝐝

                                                = 3 x 10⁸ m s⁻¹/2.42

                                                = 1.24 x 10⁸ m s⁻¹

The speed of light in vacuum (3 x 10⁸ m s⁻¹) reduced to (1.24 x 10⁸ m s⁻¹) in diamond.

The refractive index of water is 4/3 and that of glass is 3/2. What is the refractive index of glass with respect to water?

Given:

Refractive Index of Water n𝐰𝐚𝐭𝐞𝐫 = 4/3

Refractive Index of Glass n𝐠𝐥𝐚𝐬𝐬   = 3/2

We Know,  n𝐰𝐚𝐭𝐞𝐫 = Speed of Light in Vacuum/Speed of Light in Water  = c/v𝐰

Similarly, n𝐠𝐥𝐚𝐬𝐬 = Speed of Light in Vacuum/Speed of Light in Glass    = c/v𝐠

To find refractive index of glass with respect to water.

n𝐠𝐰 = Speed of Light in Water/Speed of Light in Glass  = V𝐰/V𝐠

n𝐠𝐰 = n𝐠𝐥𝐚𝐬𝐬/n𝐰𝐚𝐭𝐞𝐫

         = 3/2 ÷ 4/3

         = 9/8