Index of Refraction and the Wave Aspects of Light

The index of refraction of an optical material or simply
refractive index
, which is denoted by n, plays an important role in geometric optics. Refractive index is defined as the ratio between the speed of light c which is in vacuum to the speed v in that material, i.e,

Where n is the refractive index of the medium.

The velocity of light is maximum in vacuum and its velocity tend to decrease in other mediums. Thus, from the above expression, it is clear that the minimum value of n is unity. The refractive index is always greater than unity. Since the refractive index is the ratio between two similar quantities, it is dimensionless. The speed of light in vacuum is a constant, so n is inversely proportional to the speed of sound in that medium. It is only that when light passes from one medium to another of different refractive index, the direction of propagation changes. But is there any possibility of the wave nature of light also change?

The frequency  of light wave does not change while passing from one material to another, i.e, the number of full wave cycles per unit time must equal the number leaving per unit time. This is due to the fact that the boundary surface cannot create or destroy any waves. Only the wavelength of the light change. This is due to the fact that in any material the speed of sound    , where   is the wavelength. As the frequency remains the same, wavelength changes. Since, the velocity of light in any medium is very well less than that in vacuum, the wavelength of light in any medium other than vacuum is less. Since the frequency is the same for any medium, from the above discussion,

Here   is the wavelength of light in vacuum.

Since, , we also have,


Now, let us consider two medium A and B of refractive index nA and nB such that nA > nB. So, the speed of light is less in A medium than in medium B and the corresponding wavelengths are


Since nA > nB so . It the situation is just reversed, i.e, nA < nB we shall have .

The conclusion can be drawn from here that the waves get “squeezed” or the wavelength gets shortened if the wave speed decreases and get “stretched” or the wavelength gets elongated if the wave speed increases.

  1. The refractive index of any medium is defined as the ratio between the wavelength of light in vacuum to that in the medium.

What is the frequency of light in that medium.





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February 14, 2018

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