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Total internal reflection occurs when light entering at an interface between two different mediums is reflected within the medium without refraction, diffusion, transmission, scattering, or other related processes.
The ray of light cannot leave and enter the other medium in this case; instead, it is reflected into the first medium. As a result, the light ray becomes trapped within the medium’s internal structure. Total internal reflection occurs in various electromagnetic, sound, and water waves.
What is Total Internal Reflection?
Total internal reflection (TIR) refers to the complete reflection of light within a transparent medium. This is when the light is reflected by a transparent medium and comes back to the same medium. Total internal reflection happens when the incidence angle exceeds critical angle. TIR will not occur if such angle of incidence equals to or less than the critical angle.
The Prerequisites For Total Internal Reflection
Total internal reflection (TIR) occurs when all incidents’ light is reflected off a barrier. TIR exists only when the following two criteria are satisfied:
The light ray must be moving from a denser medium to a rarer medium; that is, the first medium’s refractive index must be greater than the second medium’s.
The angle of incidence should be higher than the critical angle, as defined by Snell’s law.
Total Internal Reflection Equation and Formula
When a light ray reaches a medium with a lower index of refraction, it bends away from the normal and comes back, resulting in an exit angle higher than that of the incident angle. This kind of reflection is called “internal reflection.” For TIR, the critical incident angle is θc, the exit angle will approach 90°; the total internal reflection will occur for the angle of incidence higher than the critical angle.The above figure illustrates schematically how TIR occurs at the interface of two mediums. Whenever an incident light beam (red) collides with an interface, this is reflected (green) and refracted (blue).
At the interface between two materials, Snell’s law states the angle of refraction:
n1⋅sin(θ1)=n2⋅sin(θ2)
This is seen in Figure (a): wherein n1 and n2 are the material-specific refractive index.
If we make the assumption that object 1 is in water (n1=1.3) and object two is in the air (n2=1.0),
θ’ is more significant than θ as n1>n2, and
θ’ will become π /2 (i.e. 90 °) for that incident angle θ = θc.
This angle is referred to as the crucial angle. It can be calculated using the following total internal reflection formula:
θc=sin−1(n2/n1).
Light can no longer be refracted at an angle θ > θc. Hence it is reflected by the object one totally (water).
Snell’s law can be used to determine the critical angle by setting the refraction angle to 90°. Fibre optics rely on total internal reflection used in polarising prisms.
Total Internal Reflection Applications:
1. Diamond:
The refractive index of diamonds is relatively high (n~2.42). Refraction occurs when light contacts a diamond and passes through it. However, due to the shape of the surface and its high refractive index, the light will go through multiple reflections within it before exiting. TIR is what gives diamonds their bright and sparkling appearance.
2. Optical fibre:
Optical fibre has a core (with a higher refractive index) and a covering (lower refractive index). Because the angle of light moving through the core is greater than the critical angle, it will undergo many internal reflections. An endoscope is an example of equipment that uses a collection of optical fibres.
3. Safety reflector:
A safety reflector is made up of many prisms. They are structured so that light falling on them undergoes numerous internal reflections until refracting back out.
4. Periscope:
In a submarine, a periscope is required. A periscope is made up of two triangular prisms with a right angle. They are placed so that light that enters the first prism at 90 degrees is reflected at 45 degrees. It is greater than the critical angle for the glass-air material pair. This procedure is repeated till the light enters the eyepiece for the second prism. Thus, objects visible above water can be observed from within the submarine.
5. Total Internal Reflection Microscopy (TIRM):
TIRM is an optical method that allows for the direct gap distance between a microscopic sphere and a flat plate. The sphere, which has a different refractive index than the plate, is lighted using evanescent waves. This distance is determined by the intensity of the light scattered.
When light strikes the sphere, the sphere scatters some of the light waves. The term “frustrated whole internal reflection” refers to this phenomenon. Total internal reflection fluorescence microscopy (TIRFM) extends TIRM and is a critical technique in biophysics and quantitative biology.
Example of Total Internal Reflection
Mirages are a frequent occurrence of total internal reflection in deserts, where the air density varies due to the sun’s rays heating the surface. A ray of light passing through dense cold air will be reflected by the rare hot air near the surface. So, someone standing far away can see an object’s reflection on the ground.
Conclusion
This article explains the total internal reflection of light. Total internal reflection occurs when light entering at an interface between two different mediums is reflected within the medium without refraction, diffusion, transmission, scattering, or other related processes. There are a large number of applications of TIR, such as optical fibre, total internal reflection microscopy(TIRM), etc.
