Refractive Index – Definition, Formula

Refractive Index 

Introduction

A pencil dipped in water appears to be a little displaced at the water surface. This is due to the refraction of light through water which bends the light rays on entering or emerging from water. However, this amount of bending would not remain the same when water is replaced with some other substance such as kerosene, mustard oil or clear gel etc. The amount of bending a light ray suffers on entering a substance depends upon its refractive index. 

Explanation

Refractive index: 

A ray of light traveling obliquely from one medium to another changes its direction in the second medium. The extent of the change in the direction that takes place in a particular pair of medium can be measured in terms of the refractive index, mathematically given by the Snell’s law. 

The amount of bending of the light ray on traveling from one medium to another is given by the refractive index of the second medium w.r.t the first. Refractive index is a property of a pair of mediums and not a single medium. 

Refractive index is a unitless quantity. It is denoted by ‘n.’ The greater the value of refractive index of a medium in a particular pair, the greater is the bending of light in it. 

The speed of light is different in different mediums, which gives rise to its bending. The speed of light is fastest in vacuum i.e., 3 x 10⁸ m/s and negligibly less in air. However, it reduces considerably in denser mediums such as water, kerosene and glass. The refractive index of a pair of medium depends upon the speed of light in them. 

The refractive index of the medium 2 w.r.t medium 1 is given by, 

Similarly, the refractive index of medium 1 w.r.t medium 2 is given by, 

Absolute refractive index: 

If medium 1 is vacuum or air, the refractive index of medium 2 w.r.t medium 1 is considered w.r.t vacuum. This refractive index is called the absolute refractive index of medium 2 (n). The absolute refractive index of a medium is the ratio of the speed of light in vacuum or air and in the medium. 

Where c (= 3 x 10⁸ m/s) is the speed of light in vacuum or air and v is its speed in the medium. 

Refractive index of air is,  

Here, both the first and the second medium, both are air, the velocity remains c = (= 3 x 10⁸ m/s). The refractive index of any other medium is greater than 1, as the velocity v in that medium is always less than c. As a result, n >= 1. 

Absolute refractive index of glass is,  

As here the first and the second medium, both are air, the velocity remains c (= 3 x 10⁸ m/s). 

The absolute refractive index of water can be calculated similarly to yield 1.33.  

n_water = 1.33 

n_glass > n_water 

This means that glass bends a light ray more than that of water. 

Questions and Answers: 

1. Study the table below which shows the absolute refractive indices of commonly found materials.   

a. Identify three materials which bend the light to the highest and arrange them in a descending order. 

b. How would a light ray which is traveling in alcohol and then entering a piece of crown glass bend? Give reasons for your answer. 

Answer: 

a. Diamond > Sapphire > Ruby 

b. The light ray traveling in alcohol would bend towards the normal on entering a piece of crown glass. This is because crown glass has a higher refractive index as compared to alcohol. 

2. Draw the path of the incident ray through the mediums shown in the picture in the sequence shown by drawing a normal line at every point and the refracted ray and finally the emergent ray. 

Answer:

Summary

1. The speed of light in a vacuum or air is 3 x 10⁸ m/s.
2. The light bends towards the normal on entering a denser medium in order to cover a
   shorter path in the same time, as its speed is reduced in that medium.
3. The speed of light increases to become 3 x 10⁸ m/s as it comes out of a denser medium
   back to air. Thus, it bends away from the normal.
4. A ray of light undergoes a lateral shift on passing through a glass slab after refraction.
5. Refractive index is a measure of the amount of bending or the change in speed of light
   when it enters a medium from air.
6. The absolute refractive index of a medium is the ratio of the speed of light in vacuum or
   air and in the medium. That is, n= c/v, where c is the speed of light in air and v is its
   speed in the medium.
7. The refractive index of air or vacuum is 1, which is the minimum value of all.
8. The angle of incidence is not equal to the angle of refraction, except for normal
   incidence.
9. The angle of incidence is always equal to the angle of emergence.