# Refractive Index Formula

The refractive index of a medium is defined as how the light travels through that medium. It is a dimensionless measure. It defines how much a light ray can be bent when it enters from one medium to the other. Snell’s law clarifies the relation between the angle of incidence and angle of refraction. So, there are two formulas for calculating the refractive index of a medium. Let us imagine that a ray of light is travelling from a medium a to another medium b. Then conferring from Snell’s law,

$\frac{sin\,&space;i}{sin\,&space;r}\,&space;=\,&space;n$

here n is a constant value which is recognized as the refractive index of medium ‘b’, in regards to medium ‘a’.

The refractive index has no units as it is a ratio of two similar quantities.

Refractive index of a medium is also defined as the ratio of the speed of light in air or vacuum and the speed of light in that medium. If the speed of light in air is c and the speed of light in the medium is v then the refractive index of the medium is articulated as,

$n\,&space;=\,&space;\frac{speed\,&space;of\,&space;light\,&space;in\,&space;vacuum}{speed\,&space;of\,&space;light\,&space;in\,&space;medium}\,&space;=\frac{c}{v}$

Refractive Index Solved Examples

Let us discuss the questions of the refractive index of a medium.

Problem 1: A light ray is transient through a medium to another one. The angle of incident is provided as 30° and the angle of refraction is 50°. Compute the refractive index of the second medium?

Given parameters

i (Angle of incidence) = 30° and

r (angle of refraction) = 50°

The formula for refractive index is articulated as,

$n\,&space;=\,&space;\frac{sin\,&space;i}{sin\,&space;r}\,$

$n\,&space;=\,&space;\frac{sin\,&space;30}{sin\,&space;50}\,$

$n\,&space;=\,&space;\frac{0.5}{0.7660}\,&space;=\,&space;0.6527$

Problem 2: Compute the refractive index of the medium if the speed of light in a medium is 2×108m/s?

$n\,&space;=\,&space;\frac{c}{v}$
$n\,&space;=\,&space;\frac{3\times&space;108}{2\times&space;108}\,&space;=\,&space;1.5$