Dimensional Formula of Refractive Index

The qualities of the medium affect the speed (increasing or decreasing) when light enters it. The optical density of the medium signifies the speed of electromagnetic waves. The optical density of the medium is defined as the tendency of atoms in a substance to recover absorbed electromagnetic energy. The speed of light depends on the concentration of the density of the substance – the more optically dense the substance is, the slower the speed of light will be and vice versa. The optical density is the measurement of the refractive index of a medium. The physical quantity is dimensionless.

Refractive Index

The refractive index is a metric that measures how far light rays bend when they enter another medium. The letter ‘n’ stands for refractive index.

‘n’ is a derived variable.

It’s the ratio of c and  v.

Where c is the velocity/speed of light in the air of a specific wavelength, and v denotes the speed of light in any medium.

Table: Absolute refractive index of some material media

Dimensional formula of Refractive Index

The dimensional formula refractive index can be written as:

[M0L0I0T0]

Where,

M = Mass

L = Length

T = Time

Derivation for the dimensional formula of refractive index

Refractive Index  = (Speed of light in vacuum) × 1/(speed of light in medium)

• n = c/v

Speed = Distance × 1/(Time)

• I.e S = D x T

Therefore, the dimensional formula of speed can be written as 

[M0L1T-1]

The refractive index = the ratio of the speed of light in a vacuum to the speed of light in a medium.

Therefore,

The Refractive Index = (Speed of light in vacuum) × 1 / (speed of light in medium)

 [M0L1T-1] × 1 / [M0L1T-1]

Hence,

the r dimensional representation of the refractive index can be written as 

[M0L0I0T0], 

Note: It is a dimensionless quantity.

Measurement of refractive index

The refractive index of a medium is measured with a refractometer. Refractometers come in a variety of shapes and sizes, including the Abbe refractometer. The theory behind a refractometer is that light bends when it enters a different medium. The angle of refraction of light rays travelling through an unknown substance is measured with this equipment. 

By applying Snell’s law, this measurement, along with knowledge of the refractive index of the medium directly in contact with the unknown sample, is used to determine the refractive index of the unknown sample.

Why is it necessary to calculate refractive indices?

Refractive indices serve a variety of applications, but are most commonly employed to distinguish between liquid samples. As a result, in the same way, as melting points are used to characterise solids, this physical quantity is utilised to characterise liquids. By comparing a substance’s refractive index to known literature values, this measurement can be used to identify it. Furthermore, by comparing the refractive index of a substance to that of a pure compound, refractive indices can be used to assess the purity of a chemical.

By comparing the solution’s refractive index to a standard curve, refractive indices can also be used to determine the concentration of a solute in a solution. Finally, the polarizability of a material affects refractive indices. The higher a substance’s refractive index, the more polarizable it is. As a result, knowing a substance’s refractive index is also required to compute its dipole moments.

Conclusion

The qualities of medium (optical density of the material) affect the speed of light entering by increasing or decreasing it. The optical density of the material decides the refractive index of the light in any medium it enters. The refractive index is a comparison of the speed of light in a vacuum to any other medium it enters. Different mediums ( air, water, ice, diamond, ethyl alcohol, etc) show different values of refractive index based on their optical density. The refractive index is a dimensionless quantity with no SI unit and is represented by (n).