The Refractive Index

The refractive index of second medium with respect to the first medium is defined as the ratio of the sine of the angle of incidence in the first medium to the sine of the angle of refraction in the second medium.

The refractive index of medium 2 w.r.to medium 1:

\[n_{21} = \frac{\text{Speed of light in medium 1}}{\text{Speed of light in medium 2}} = \frac{v_1}{v_2}\]

The refractive index of medium 1 w.r.to medium 2:

\[n_{12}=\frac{\text{Speed of light in medium 2}}{\text{Speed of light in medium 1}}=\frac{v_{2}}{v_{1}}\]

The refractive index of the medium n_m  is given by:

\[n_{m} = \frac{\text{Speed of light in air}}{\text{Speed of light in the medium}} = \frac{c}{v}\]

OR

\[\frac {\text{sin i}}{\text{sin r}}\] = constant = n

n is called the refractive index of the second medium with respect to the first medium.

• The incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane.
• The ratio of the sine of the angle of incidence i to the sine of the angle of refraction r is constant for the pair of given media. i.e., mathematically

\[\frac {\text{sin i}}{\text{sin r}}\] = constant = n

Where:

• i = angle of incidence
• r = angle of refraction
• n = refractive index of the second medium with respect to the first

This ratio is constant for a given pair of media and is known as the refractive index.

Note: If a light ray is incident along the normal (i = 0^∘), it passes undeviated into the second medium (r = 0^∘).