# 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 = $\displaystyle&space;\frac{c}{v}=\frac{{{{\lambda&space;}_{{vac}}}\times&space;\nu&space;}}{{{{\lambda&space;}_{{med}}}\times&space;\nu&space;}}=\frac{{{{\lambda&space;}_{{vac}}}}}{{{{\lambda&space;}_{{med}}}}}$

### 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 = $\frac{{{{v}_{1}}}}{{{{v}_{2}}}}=\frac{{{{\lambda&space;}_{1}}}}{{{{\lambda&space;}_{2}}}}=\frac{{{{\mu&space;}_{2}}}}{{{{\mu&space;}_{1}}}}$

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.