Total Internal Reflection

Total internal reflection is one of the most important optical effects of light, powering various fascinating phenomena. From natural phenomena like mirages to artificial guiding of light through fibre optics, total internal reflection is the cornerstone of many optical effects and technologies. Owing to the fact that total internal reflection is an important phenomenon, it is necessary to have a clear understanding of the conditions responsible for this, along with its other applications. This is why, in this section, we’ll try to thoroughly explain total internal reflection with an easy-to-understand approach. 

1.0Science Behind Total Internal Reflection

As known, light travelling from the rarer/denser medium to the denser/rarer medium reflects from its original path. In Total Internal Reflection (TIR), a light ray travelling from a denser medium to any other rarer medium is reflected back completely into the denser medium rather than going into the rarer medium. In simple words, instead of refracting into the second medium, the light comes back to its previous medium. This effect follows the law of reflection, stating that the angle of incidence always equals the angle of reflection.

The reason behind this internal reflection is the critical angle, which will be explained in the subsequent sections. When the angle of incidence on the rarer medium’s boundary is more than the critical angle, this phenomenon of total internal reflection occurs. 

2.0Critical Angle and Total Internal Reflection

The critical angle and total internal reflection are closely related to each other. It is the minimum angle of incidence at which light will no longer refract. Instead, it is entirely reflected within the denser medium. If the light coming from the denser medium forms a greater angle of incidence than the critical angle, then the phenomenon of total internal reflection will occur. 

For example, when a light ray travels from water (with a refractive index of about 1.33) to air (with a refractive index of 1.00), the critical angle is about 48.6°, and if the angle of incidence formed by the ray measures more than this value, you can experience a total internal reflection. The critical angle in the total internal reflection formula can be written as: 

$CriticalAngle(\theta )=si{n}^{-1}\frac{n_2}{n_1}$

Here, 

• n₁ = refractive index for the medium 1 (denser medium) 
• n₂ = refractive index for the medium 2 (rarer medium)
• $(\frac{n_2}{n_1})=\frac{Sin(r)}{Sin(i)}$, where, r = angle of refraction, and i = angle of incidence. 

3.0Refractive Index & Its Role in TIR

The refractive index of a material is a basic property of light travelling through different media. It gives the idea of the speed of light in different mediums; a denser medium results in low speed, while in the rarer medium, the light travels at a much higher speed than its counterpart. The refractive index tells us about the amount of bending of light when entering into another material. The formula for refractive index is: 

$Refractiveindex(n)=\frac{n_2}{n_1}=\frac{Sin(r)}{Sin(i)}$

As mentioned previously, TIR occurs only when the light travels from a denser to a rarer medium. Hence, at a certain critical angle, the refracted light would travel parallel to the boundary, and any further increase in the angle of incidence would cause the light to be completely reflected back into the denser medium. This is a total internal reflection.

4.0Conditions For Total Internal Reflection

For total internal reflection to happen, there are two conditions that are a must which include: 

• The light ray must travel from a denser medium, such as glass, water, etc., to a rarer medium, like air. 
• The critical angle must be less than the angle of incidence for a certain pair of media. 

5.0Applications of Total Internal Reflection

The total internal reflection is not only responsible for optical illusion, but conversely, it has made its way to some revolutionising practical applications of TIR in fields of science and technology. The ability of light to travel with the minimum loss of energy has made this phenomenon of light the best source of energy in a wide range of industries, which includes: 

• Optical Fibers and Total Internal Reflection: Optical fibres consist of a core that has a high refractive index, and materials with a lower refractive index surround it as cladding. Once injected into the core, the light undergoes numerous total internal reflections and travels down the fibre with confinement into the core irrespective of the bending or twisting of the fibre.
• Prisms and Optical Instruments: Periscopes, which are frequently found in submarines or other optical devices, use TIR to make sure that light is directed through a set of mirrors or prisms so that users may see above obstructions. Using TIR, prisms in binoculars and telescopes focus light through the lens system to provide clean, clear images free from distortion or light leakage.
• Medical Applications: In medical diagnostics, total internal reflection is also commonly used, especially in endoscopy. Doctors can view inside organs and tissues without making big incisions using total internal reflection to steer the light that illuminates the area being investigated through flexible optical fibres.

6.0Examples Of Total Internal Reflection

• Mirages: In warm conditions or summers, the temperature of the surface air rises, causing a decrease in the density of air. This density difference makes light undergo total internal reflection with the bending of light and making objects displaced, creating an illusion. 
• Brilliance of Diamond: A characteristic feature of a diamond is its shining property. The reason behind this brilliance is also the total internal reflection. A diamond's high refractive index causes light entering from the air to slow down. As a result, light is bent (refracted) at the diamond-air interface.