Light: Refractive Index

These notes are based on the chapter Light: Reflection and Refraction from class 10 science NCERT book and CBSE syllabus

A ray of light changes its direction when it enters from one medium to another medium. This happens because speed of light is different in different media. For example; the speed of light is 3 x 10⁸ m/s (2.99x10⁸ m/s) in vacuum and it is 2.98 x 10⁸ m/s in air.

Refractive Index is the extent of change of direction of light in a given pair of media. The refractive index is a relative value of speed of light in the given pair of media. Thus, to calculate the refractive Index the speed of light in two media is taken.

Let the speed of light in medium 1 is v₁ and in medium 2 is v₂

Therefore; refractive index of medium 2 with respect to medium 1 (n₂₁)

`n_(21)=text(Speed of light in medium 1)/text(Speed of light in medium 2)`

Or, `n_(21)=(v_1)/(v_2)`

Above expression gives the refractive index of medium 2 with respect to medium 1. This is generally denoted by n₂₁.

Similarly, the refractive index of medium 1 with respect to medium 2 is denoted by n₁₂.

`n_(12)=text(Speed of light in medium 2)/text(Speed of light in medium 1)`

Or, `n_(12)=(v_2)/(v_1)`

Absolute Refractive Index

When one medium is taken as vacuum and speed of light is taken in it, then the refractive index of second medium with respect to vacuum is called Absolute Refractive Index and it is generally denoted by n₂.

Thus, `n_2=text(Speed of light in vacuum)/text(Speed of light in given medium)`

The speed of light in vacuum is slightly faster than in air. Let speed of light in air is ‘c’ and the speed of light in given medium is ‘v’. Therefore, refractive index of the given medium:

Thus, `n_m=text(Speed of light in air)/text(Speed of light in given medium)=c/v`

Since, Refractive Index is the relative value of the speed of light of a medium with respect to the speed of light in vacuum, thus light will travel faster in the medium having lower value of refractive index.

Optical Density

Medium having greater value of refractive index is called optically denser medium, this means light will travel at slower speed in optically denser medium compared to in an optically rarer medium.

Applications of Refractive Index

Refractive index is an important property of the components of any optical instrument such as binocular or telescope.
Refractive index determines the focusing power of lenses.
Refractive index determines the dispersing power of prism.
Refractive index determines the light-guiding nature of optical fibre.
Refractive index is used to identify a particular substance and purity of a substance.