Total Internal Reflection and its applications

Internal reflection often occurs when  a light beam or ray travels from a denser medium to a rarer or less optically denser medium. 

In such a phenomenon, two things happen. A portion of the incident light gets reflected into the same medium. In contrast, another part gets refracted into a different medium. 

When the angle of incidence made by the incident ray is greater than the critical angle, the phenomenon is known as total internal reflection.    

Total Internal Reflection Explanation with Example

When a light ray travels from a medium with more optical density to a less optically denser medium, the beam gets bent away from the normal. This behaviour, in turn, makes the angle of refraction more than the angle of incidence.

Let us take an example to discuss total internal reflection in detail. Consider water and air as the two mediums in which the refraction of light takes place. Let water be medium 1 and air be medium 2. We will now look at how to calculate the critical angle.

The Formula of the Critical Angle 

We can find the value of the critical angle using Snell’s law:

n1n2=sin(r)sin(i)

Where, 

r is the angle of refraction, which is 90°

i is the angle of incidence

n1 is the refractive index of the first medium (water)

n2 is the refractive index of the second medium (air) 

Here is the formula of critical angle in the sine form:

sin() = n2n1

We can define the formula form of the critical angle as:

The sine of the critical angle is equal to the ratio of the refractive index of the second medium to the refractive index of the first medium. 

Necessary Conditions for Total Internal Reflection 

For total internal reflection to occur, the light must satisfy the two conditions mentioned below: 

1. The incident light beam should travel from a more dense medium to a rarer medium. 
2. The critical angle should always be less than the angle of incidence (made by the incident ray). 

Total Internal Reflection and Its Applications

Some critical applications of total internal reflection are:

• Diamond 

Diamonds are famous because of their fantastic shine and glamorous look. 

The brilliance of a diamond is due to the phenomenon of total internal reflection. The beam of lights entering the diamond suffers multiple internal reflections and shines. The diamond’s cut plays a role in enhancing this lustre.  

• Mirage 

A mirage is an optical illusion concept based on total internal reflection. You can observe this optical phenomenon during the hot summer days. According to this phenomenon, the air near the ground gets hotter than that at high altitudes.  

While hot air has a small refractive index and is less dense, cold air has a large refractive index and is denser. Thus, with the increase in height, the optical density also increases. 

When a light beam passes through a denser object, the light bends away from the normal and undergoes total internal reflection. 

Hence, when you walk or drive on hot sunny days, sometimes you will find that the light coming to your eyes originates from the ground. It results in the inverted image of tall objects in the water, and the phenomenon is known as a mirage.  

• Optical Fibre 

Another important application of total internal reflection is the concept of optical fibre. In this, when a beam of light strikes the cladding, total internal reflection occurs. Here, the formed angle is always more than the critical angle.

The refractive index of the cladding material is lower than the refractive index of the core material. When the beam of light moves from one end of the optical fibre to another at a certain angle, it undergoes total internal reflections. This reflection happens in the entire fibre, and then the light comes out from the other end.  

Uses of Optical Fibres

These fibres can transmit and receive electrical signals. We can convert these electrical signals to light with the help of a transducer. 

Another instrument that uses optical fibres are light pipes. These instruments help doctors and other healthcare professionals to examine the internal organs of the human body. 

Conclusion 

When a light beam travels from one medium to another medium which has a different refractive index, then the light beam deflect from its path, this is called refraction of light.. This refraction happens at the junction point of the two media. 

During the refraction, the light ray bends away from the normal, increasing the angle of refraction. At a certain angle of incidence, the incident light ray passes straight along the transparent surface. This specific angle of incidence is termed as critical angle denoted by C and is always 90°. 

There are also some events where the critical angle is less than the angle of incidence. The light experiences a total reflection in the same medium in such a case. This phenomenon is known as total internal reflection.