Refractive Index

Refractive Index

Refractive Index in terms of Speed of Light

The refractive index of a medium may be defined in terms of the speed of light as follows

Refractive index = \frac{{Speed\,\,of\,\,light\,\,in\,\,vacuum}}{{Speed\,\,of\,\,light\,\,in\,\,medium}}$

or   µ = \frac{c}{v}$

Refractive Index in terms of Wavelength

Since the frequency (n) remains unchanged when light passes from one medium to another, therefore,

µ = \displaystyle \frac{c}{v}=\frac{{{{\lambda }_{{vac}}}\times \nu }}{{{{\lambda }_{{med}}}\times \nu }}=\frac{{{{\lambda }_{{vac}}}}}{{{{\lambda }_{{med}}}}}$

Relative Refractive Index

The relative refractive index of medium
2 with respect to medium 1 is defined as the ratio of speed of light (v1) in the medium 1 to the speed of light (v2) in medium 2 and is denoted by 1µ2.

Thus,    1µ2 = \frac{{{{v}_{1}}}}{{{{v}_{2}}}}=\frac{{{{\lambda }_{1}}}}{{{{\lambda }_{2}}}}=\frac{{{{\mu }_{2}}}}{{{{\mu }_{1}}}}$

As refractive index is the ratio of two similar physical quantities, so it has no unit and dimension.


Factors on which the refractive index of a medium depends are :

      (i)   Nature of the medium.

(ii)  Wavelength of the light used.

(iii) Temperature

(iv) Nature of the surrounding medium.

It may be noted that refractive index is a characteristic of the pair of the media and also depends on the wavelength of light, but is independent of the angle of incidence.