Refractive Index

The refractive index is a common phenomenon, which is being observed almost daily.

A light ray changes its direction when it travels from one medium to another medium. It happens due to the variation in the speed of light in each medium. The speed of light in a vacuum is \[3\times10^{8}\] meters/second, and the speed of light in air is\[2.98 \times10^{8}\] meters/second. 

The refractive index/index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of the light in the medium. The value of the refractive index varies from one medium to another. In other words, the refractive index is the measure of the bending of the light ray during the travel from one medium to another medium.

The Phenomenon of Refraction Deals with Two Aspects:-

• Speed of the light in the medium

• Angle of Refraction

Calculation of the Speed of Light

To calculate the refractive index, the speed of light is considered in two mediums. The symbol "n" denotes the refractive index.

Speed of Light in the 1st medium - v₁

Speed of light in the 2nd Medium- v₂

Now, the refractive index (n) of 2nd medium with respect to 1st medium is:-

 n₂₁= Speed of Light in 1st medium/ Speed of light in 2nd medium 

Or, we can say:-

n₂₁ = v₁/v₂                                   

Now, the refractive index (n) of 1st medium with respect to 2nd medium is:- 

n₁₂ =. Speed of Light in 2nd medium/ Speed of light in 1st medium              

Or, we can say:-

n₁₂ = v₂ / v₁

Absolute Refractive Index

As mentioned before, to calculate the refractive index, two different mediums are considered. But, when one of the two mediums is considered a vacuum, then the refractive index of the second medium, concerning the first medium, is known as Absolute Refractive Index. The symbol n denotes the absolute Refractive Index.

Therefore, n = Speed of Light in Vacuum/Speed of light in the medium 

The speed of the light is faster in a vacuum compared to the speed of the light in air. 

Assume the speed of the light in the air as "c," and that of the given medium is "v." Then, the refractive index of the given medium is calculated as:- 

n = Speed of Light in Air/ Speed of light in given medium

n = c/v                   

For example, the water refractive index is 1.33, which means the speed of light in water is 1.33 times lesser than the speed of light in a vacuum.

Optical Density

An optically denser medium is a medium, which has a higher value of the refractive index. This means the speed of the light is slow in the optically denser medium in comparison to an optically rarer medium.

Snell’s Law - Calculation of Angle of Refraction

The refractive index also determines how much the light changes its path when it travels from one medium to another medium. Snell's law explains this angle of refraction. Snell's law is also known as "Law of Refraction" and “Snell-Descartes” Law. Willebrord Snell discovered Snell's Law in 1621.

When the light hits the barrier between two mediums, then the light is partly refracted and partly reflected. Snell's law explains the relation between the angle of incidence and angle of refraction when the light passes through one medium to another, such as air, glass, water.

The ratio of the sine of the angle of incidence and sine of the angle of refraction is identical to the ratio of the phase velocity in two different media. Moreover, it is also identical to the ratio of indices of the refraction.

\[\frac{Sin\theta _{2}}{Sin\theta _{1}} = \frac{v_2}{v_1} = \frac{n_1}{n_2}\]

Here, 

• Every θ is calculated from the line perpendicular to the boundary of the surface (normal)

• v - Velocity of light with respect to each medium

• n - The refractive index with respect to each medium

Snell’s law is applied to isotropic media (where most of the values are not dependent on directions in general).

Practical Applications of the Law of Refraction

1. Optical instruments such as spectacles, lenses, and other instruments.

2. Camera Lenses: It is desirable to know how much light will change its path from a camera lens. This helps in a correction of the position of the object.

3. Contact Lenses: As a wearable lens, the contact lens also needs to be calibrated according to each person’s eyesight.

4. Liquids: There are specific instruments used to calculate refraction occurring in liquids. This is helpful while mixing two liquids in industries and while creating certain kinds of candies.