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Refractive Index - Formula, Definition, Material Table and Snell’s Law

The Refractive index of a material is a dimensionless ratio that describes the speed of light inside that material in terms of its speed in vacuum. It is also called the refraction index or index of refraction of a material. The refractive index of a material determines how much the incoming beam of light will be bent (refracted) when passing through that material. The value of the refraction index of a substance is derived by dividing the velocity of light in vacuum by the phase velocity of light in that medium, and the expression for the refractive index is given as follows. n = c / v where

  • n = the refractive index of that material
  • c = the speed of light in a vacuum
  • v = the phase velocity of light in that medium

From the formula and definitions of the refractive index of a material, it can be understood that the refractive index value for vacuum is 1. This means that light can pass through a vacuum without any loss in its speed. Another characteristic of the refractive index of the material is that it does not affect the frequency value of the incoming wave since the value for frequency is given by the formula f = v/ λ where

  • f is the frequency of the incoming wave
  • v is the velocity
  • λ is the wavelength of the incoming wave

However, the refractive index depends on the wavelength of the incoming wave since the speed of light is given by the product of its wavelength and frequency. So the wavelength of the incoming light wave varies depending on the extent of refraction. This is why when light enters a suitable material, like a prism, the monochromatic white light is split into its seven wave constituents, each with its very own color and unique wavelength values. This phenomenon is called dispersion, and rainbows are a product of this phenomenon. The minute water droplets, ice crystals, and other particulates disperse the incoming sunlight, creating a rainbow.

The phenomenon of refraction can be observed for all kinds of waves in the electromagnetic spectrum and even for mechanical waves such as sound waves. However, if refraction of sound waves is to be determined, the speed of sound and a suitable reference medium must be considered because sound waves cannot travel in the absence of a medium. Refraction can also be observed in the case of materials that tend to absorb the incoming light. Here, a complex-valued refractive index system is used where the real part value corresponds to the refraction in that material while the imaginary part value corresponds to the attenuation. Let us consider a block of household glass, which has a refractive index of approximately 1.6. This means that inside this block of glass, the light will travel 1.6 times slower compared with its speed in a vacuum. If a material has a higher refractive index relative to another material, that material is said to be optically dense.

So, the higher the refractive index, the optically denser is the material. When designing an optical component, the knowledge of the refractive index of the materials involved is very helpful. In the manufacturing of eyeglasses, materials with a high refractive index are preferred because this would mean thinner lenses, thus, effectively bringing down the overall weight of the eyeglasses.

The refractive index of some materials are given below.

Material

Refractive index (n)

Vacuum

1

Air

1.000 293

Helium

1.000 036

Carbon dioxide

1.000 450

Water

1.333

Olive oil

1.47

Ice

1.31

Window glass

1.52

Polycarbonate

1.58

Diamond

2.42


 

Snell’s Law

Snell’s law provides an expression that interrelates angles of incidence and angle of refraction, the refractive indices, and the speed of a wave when it enters a different medium from another medium, each with its unique refractive index values. Also called Snell–Descartes law and the law of refraction, Snell’s law states that the ratio of the sines of the angle of incidence and angle of refraction is equal to the ratio of the phase velocities in the two different media and also equal to the reciprocal of the ratio of the indices of refraction in those two different media.

(Sin Ɵ2/ Sin Ɵ1) = v2/ v1 = n1/ n2


where

  • Ɵ 1 is the angle of incidence of the wave.
  • Ɵ 2 is the angle of refraction of the wave.
  • v 2 is the phase velocity of the wave in medium 2.
  • v 1 is the phase velocity of the wave in medium 1.
  • n 1 is the refractive index of medium 1.
  • n 2 is the refractive index of the medium 2.
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