Definition

Refractive index is defined as how the light travels through that medium. It is dimensionless.This is the measure of how much a light ray bends when leaving one medium and entering another. It defines Snell's law about the angle of incidence being related to the angle of refraction. As a result, there are two equations that can be used for determining the refractive index of a medium. We assume that a ray of light is traveling from medium 'a' to another medium 'b'. Now, if we refer to Snell's law,

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

Formula 

Refractive index of a medium is also expressed 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 expressed as,

Where, 

• n: refractive index

• c: speed of light in a vacuum 

• v: speed of light in the medium
  

Refractive Index Solved Problems

Problem 1: A light ray is passing through a medium to another one. Angle of incidence is given as 30° and angle of refraction is 50°. Calculate the refractive index of second medium?

Solution :

Data Given

          i (angle of incidence) = 30° and

          r (angle of refraction) = 50°

 The formula for refractive index is written as,

     n = sin i / sin r

     n = sin 30 / sin 50

     n = 0.5/0.7660

     n = 0.6527

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

Solution:

It is given by,

The formula for the refractive index of the medium is given by,

                   

 

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