Introduction to Total Internal Reflection
The optical phenomenon of total internal reflection occurs when light is entirely reflected at the interface between two media.
The effect happens when the incidence angle exceeds a predetermined limiting angle, referred to as the critical angle.
Let’s take an example for more clarity.
When an incident light ray hits the interface, it is reflected and/or refracted.
A ray of light travels from a medium of water to a medium of air, and vice versa. Light Rays will be refracted at the interface that separates the two media.
The refracted light ray bends away from the normal as it passes from a medium with a higher refractive index to one with a lower refractive index.
The incident ray of light is refracted in such a way that it passes down the water's surface at a given angle of incidence known as the critical angle.
The refraction angle is now 90 degrees and the incident light can reflect on the medium if the angle of incidence is greater than the critical angle.
As a result, this phenomenon demonstrates to be a total internal reflection.
What is Total Internal Reflection?
Total internal reflection happens at a time when a light ray that travels from a denser to a rarer medium. The ray is incident at an angle of incidence that is greater than the critical angle. After that, the light rays are reflected in another denser medium. It is the same medium before reflection. The entire process is known as Total internal reflection.
When light travels between two surfaces made of transparent materials, then it gets refracted. This is also called as the bending of light. Light or rays that come towards or drive away from the normal have interfered. This happens due to a change of one medium to another medium. This gives the simple definition of total internal reflection.
When does Total Internal Reflection Take Place?
Take the example of two lights that incident at certain points from an optically denser medium to an optically rarer medium.
The bending of light, i.e. from the normal happens under the phenomena called refraction of light. This is a special condition where the refracted angle is more than the incident angle.
The above statement explains that the increase in the angle of incident results in the increment of the angle of refraction.
A point still exists where the angle of refraction becomes perpendicular. When this happens, the refracted ray will become parallel to the interface.
The incident ray angle of the denser medium corresponding with the refracted ray angle of the rarer medium is 90o. This is called the Total internal reflection critical angle(ic).
That time when the ray is incident on the surface at an angle greater than the critical angle, the ray comes back to the same medium. The entire procedure of returning a light ray away from the denser medium is known as Total Internal Reflection.
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Explain Total Internal Reflection of Light
We have two major conditions that help us to decide the phenomenon of total internal reflection. (TIR) is based upon. The minor change in the two conditions may not give the appropriate result.
Total internal reflection has 2 necessary conditions such as:
(i) The light incident upon the interface of two different media should choose to travel from a denser medium to another rarer medium.
(ii) The greater angle of incidence is necessary than the critical angle for these two media.
The formula and Applications of Total Internal Reflection
Formula:
Snell's law determines the angle of refraction at the interface of two materials.
n1⋅sin(θ) = n2⋅sin(θ′)
Where,
n1 and n2 = Refractive indices of the two materials
θ = Incident angle of light
θ’ = The angle of refraction
So, now if suppose
Material 1 is water (n1 = 1.3)
Material 2 is air (n2 = 1.0)
θ’ is greater than θ as n1 > n2
θ’ becomes π /2 (i.e. 90o) for a certain incident angle θ = θc.
This angle is known as the critical angle, and it may be calculated using the following formula:
Θc = sin−1 (n2/n1)
Now, at an incident angle θ > θc, Light is completely reflected in material 1 (water) since refracted light can no longer exist.
To make this simple just imagine if you dive into a swimming pool and attempt to see above the surface of the water, you will be unable to see outside the water at a shallow angle.
Applications
Optical fibers
Fiber optics uses total internal reflection, which has many advantages in telecommunications. Fiber optics are light-travelling glass or plastic threads the size of a hair.
When light contacts the core-cladding boundary at an angle of incidence larger than the critical angle, it is refracted back into the core. As a result, light can travel many kilometers with little energy loss.
Endoscope
An endoscope is a medical device used for diagnostic and surgical procedures. It has two fiber-optic tubes in a pipe.
The light enters the patient's organ through one of the endoscope's fiber tubes and is then reflected by the physician's viewing lens through the outer fiber tube thus confirming total internal reflection.
Prisms
A few examples of optical equipment that use right-angled prisms to reflect a light beam through 90° or 180° are as below:
Cameras, Binoculars, Periscope, and Telescope.
Apart from these instances, the total internal reflection phenomena can be applied in a variety of other contexts and with a variety of diverse applications.
Practical Applications of Total Internal Reflection
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Optical Fibre
Total internal reflection method is used in optical fibre. The inner part of the fibre lies inside the core of the higher refractive index. All of these fibres are surrounded by another layer of glass. They lie just beneath the lower refractive index. A plastic jacket is there to surround the fibres.
Back to back total internal reflection occurs when the light from one end of the core travels toward cladding, and the light propagates through it. Optical fibres usage is quite popular among decorative table labs. They have huge applications in the medical field for endoscopy.
Mirage
Mirage is also known as another name called optical illusion of water. You must have seen this during the summer. The appearance of mirages is quite higher in the deserts on a hot summer day.
Mirage occurs when a ray of light falls on earth by travelling from the top of a tree or sky; it gradually deviates away from the normal. We know that total internal reflection exists when the angle of incidence becomes greater than the critical angle. So this generates mirage in hot deserts or any open spaces during the hot summer.
FAQs on Total Internal Reflection
1. What is Total Internal Reflection (TIR)?
Total Internal Reflection is an optical phenomenon that occurs when a ray of light, travelling from a denser medium to a rarer medium, strikes the boundary between the two media at an angle of incidence greater than a specific angle known as the critical angle. Instead of refracting into the rarer medium, the light is completely reflected back into the denser medium.
2. What are the two essential conditions required for Total Internal Reflection to occur?
For Total Internal Reflection to take place, two conditions must be met:
- The light ray must travel from an optically denser medium (like water or glass) to an optically rarer medium (like air).
- The angle of incidence in the denser medium must be greater than the critical angle for that pair of media.
3. What is the importance of the critical angle in Total Internal Reflection?
The critical angle is the specific angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90 degrees. It acts as a threshold: if the angle of incidence is less than the critical angle, light refracts. If it is greater, Total Internal Reflection occurs. It is inversely related to the refractive index; a higher refractive index means a smaller critical angle.
4. What are some common real-life examples of Total Internal Reflection?
Total Internal Reflection is responsible for several natural and technological phenomena. Key examples include:
- The brilliant sparkle of a diamond, which traps light inside through multiple TIRs.
- The functioning of optical fibres used in telecommunications and medicine (endoscopy).
- The formation of a mirage on hot days, where light from the sky reflects off a layer of hot, less dense air near the ground.
- The use of reflecting prisms in high-quality binoculars and periscopes to change the path of light without using mirrors.
5. What is the difference between regular reflection and Total Internal Reflection?
Regular reflection, like from a mirror, can occur at any angle of incidence and typically involves some absorption of light, meaning not all light is reflected. In contrast, Total Internal Reflection only happens under specific conditions (denser to rarer medium and angle greater than critical angle) but reflects nearly 100% of the light. This makes TIR a much more efficient way to reflect light.
6. How does Total Internal Reflection explain the brilliance of a diamond?
A diamond has a very high refractive index (around 2.42), which gives it a very small critical angle (about 24.4°). When light enters a properly cut diamond, it strikes the internal facets at an angle greater than this critical angle. As a result, the light gets trapped, undergoing multiple Total Internal Reflections before it exits through the top, creating the intense sparkle and fire that diamonds are known for.
7. Can Total Internal Reflection happen when light travels from a rarer to a denser medium? Why or why not?
No, Total Internal Reflection cannot occur when light travels from a rarer to a denser medium. This is because when light enters a denser medium, it bends towards the normal. Consequently, the angle of refraction is always smaller than the angle of incidence. It is impossible for the refracted ray to reach an angle of 90°, which is the required condition to define a critical angle and achieve TIR.
8. Why are optical fibres a key application of Total Internal Reflection?
Optical fibres are a revolutionary application of TIR. They consist of a central core made of glass with a high refractive index, surrounded by a cladding with a lower refractive index. Light signals sent into the core strike the core-cladding boundary at a steep angle, which is always greater than the critical angle. This causes the signal to undergo continuous Total Internal Reflection, allowing it to travel over very long distances with minimal loss of energy or data.
9. What would happen if the cladding of an optical fibre had a higher refractive index than its core?
If the cladding had a higher refractive index than the core, the optical fibre would not work. This arrangement violates the first fundamental condition for TIR, which requires light to travel from a denser medium (higher refractive index) to a rarer one (lower refractive index). In this incorrect setup, light would simply refract out of the core into the cladding and be lost, failing to propagate along the fibre.
