Total Internal Reflection: Conditions to Occur and Major Applications Explained

Table of Contents

Definition of Total Internal Reflection

Total Internal Reflection (TIR) is also one of the phenomena of refraction which sends the incoming rays of light passing from one medium to another again back to the initial medium. It is a condition that occurs when the incident ray bends so much that it crosses the boundary between the two media to pierce through the same first medium. So, literally the light has to bend a lot, away from the normal. To bend away from the normal, light has to enter from denser to rarer medium, which is the first requirement for Total Internal Reflection.

Other normal reflections only happen when the light is wandering through the same medium. However for TIR to occur, the light struggles through a lot of refraction while entering another medium and finally reaches its home medium. Since the initial and final medium is the same, it is termed as ‘Reflection’, but don’t get confused with the fact that it is a process achieved after refraction. This occurs frequently in nature and studying this law has made it possible to create advanced discoveries like optical fibers and telescopes in the field of optics.

Conditions Required for Total Internal Reflection

To achieve total internal reflection, following criterias must be satisfied:

Light must travel from a denser medium to a rarer medium.
The angle of incidence must be greater than the critical angle.

Not meeting anyone of these results a failure for our detection. If the light is moving from rarer to denser medium, the deflection of light points towards the normal and hence there is no chance of that strong deflection. Thus, the question of returning to the same medium doesn’t arise.

Similarly, if the angle of incidence can get the degree just equal to the critical angle, the light only hovers around the margin, still being unable to cross the boundary and not meeting our expectation of seeing a TIR.

Thus, understanding these conditions are the strong requirements for designing technologies like fiber optics, optical instruments, and also some sorts of sensors. The beautiful glittering of certain crystals, stars and also interesting illusions like Mirage are sensed due to Total Internal Reflection. These criteria may be simple to hear but they give us the idea on how light remains trapped under certain boundaries and sets free.

Critical Angle and How to Calculate It?

This is a specific angle formed when the refracted ray grazes along the boundary between the two media. Beyond this angle, refraction is altered and finally on reaching the same medium, light again follows reflection completely. The critical angle θc can be calculated using Snell’s Law:

Sin⁡θc = μ2/μ1

Where:

μ1 = refractive index of the denser medium,
μ2= refractive index of the rarer medium.

Note: This formula is valid only when n1>n2.

This calculation is a ground step for the prediction of total internal reflection. It is vital for engineering applications and optical designs.

Snell’s Law and Its Link to Total Internal Reflection

The refractive indices of two media are related by the formula of Snell’s law,

μ1sin⁡θ1=μ2sin⁡θ2 [Equation 1]

Where:

μ1,μ2 = refractive indices of the first and second medium,
θ1, θ2 = angles of incidence and refraction.

When Snell’s Law is applied to light traveling from a denser to a rarer medium, we find that θ2 increases more as θ1 increases. The refracted ray goes over the boundary when θ2 reaches 90°, and the critical angle is equal to θ1. After this point, the refraction falls down and the process is fully an internal reflection with no value of θ2 satisfying Snell’s Law.

Thus, Snell’s Law establishes a requirement for TIR. It helps to predict the limits beyond which total reflection takes place.

Refraction vs Total Internal Reflection: Key Differences

Refraction and Total Internal Reflection (TIR) go through the same changes in the direction of light as rumouring through two different media. However, this changes may be drastic and both phenomena may slightly differ from each other :

Refraction

Occurs when light passes from one medium into another.
The bending always occurs no matter whether the medium is denser or rarer.
Some energy is always transmitted into the second medium.

Total Internal Reflection

Special case of refraction occurring only when light passes from denser to rarer medium.
Requires the angle of incidence to be greater than the critical angle.
100% of energy transmits to the original denser medium, no portion of light found in the rarer medium.

At last, refraction confines light in the second medium whereas, TIR sets no limit on light and lets it escape freely to its original medium.

Fiber Optics: Guiding Light via Total Internal Reflection

One of the most important application areas of total internal reflection is in fiber optics. The fiber-cables are designated in such a way that a high-refractive-index core is wrapped by lower-refractive-index covers to make light undergo a continuous TIR, at an angle larger than the critical angle.

With this technique, light travels in desired great distances with little minimum loss in the energy they carry. Fiber optics are used in:

Telecommunications: Transmitting data signals globally and reliably.
Internet services: Delivering high-speed data transfer.
Cable connections: For signal distribution in desired networks.
Medical imaging: Providing optical imaging for endoscopy and diagnostic tool usage.
Sensors: Detecting strain, temperature, and pressure changes.
Space Appliance: For communication support of the satellites.

Fiber optics has completely changed the way of sending and receiving information world-wide. Modern digital communication, such as high-speed internet, television, and phone conversations, is made possible by the sole usage of Total Internal Reflection.

Prism Uses in Binoculars, Periscopes, and Cameras

Prisms, being transparent objects having certain angles at the corners, reflect or refract light. The viewing and imaging devices like binoculars, periscopes, and cameras, rely on TIR for their proper functioning.

Binoculars:

They use Porro or roof prisms to invert and revert images desirably. The prims control the light flow using TIR correctly to locate the views without using large lenses.

Periscopes:

Periscopes are used by soldiers or in submarines. They have right-angled prisms to focus light in a zigzag manner. Hence, TIR is produced which gives high intensity and distortion-free images.

Cameras:

Certain camera lenses have prisms in order to produce TIR that redirect light into the eyepiece. It provides a more accurate and compact structure.

Producing TIR in place of using mirrors in these instruments provides better resolution and prevents interruption in light by absorption. Therefore, prisms are very useful parts of optical tools.

Diamond Sparkle Explained by High Refractive Index and TIR

Because of the high refractive index of diamonds (about 2.42), they give 100% internal reflection. This makes the crystal attractive with dazzling and shining effects. Light, on passing through diamond bends and slows significantly.

This phenomenon is referred to as “brilliance” for the beautiful crystal. Furthermore, diamonds add “flame” to their looks by scattering light into many colors. The majority of the light escapes through the top which is called the crown for diamond, which is visible to the observer. For the maximum brilliance, jewelers cut diamonds at accurate angles giving maximum internal reflections.

Atmospheric Mirages and Other Natural TIR Phenomena

Mirages are another visible illusion brought up by natural TIR. The produced images are that of the sky. However, we see it like a pool on the surface of hot roads or deserts.

How is Mirage formed?

On a hot day, air near the ground becomes hotter and less dense than air upwards.
Light passing from cooler air to hotter air strongly deviates.
After exceeding critical angle, TIR is produced giving an image like of water.

Other natural phenomena of TIR are:

Fata Morgana: A complex mirage over the horizon.
Shimmering effects on lakes at sunset due to temperature fluctuation on the layers of air.
Bright streaks on fish scales or butterfly wings, results from TIR.

These natural examples prove that TIR has no limits and are not the outcomes of man-made technologies.

Endoscopy and Laser Surgery: Medical Applications of TIR

In the medical field, total internal reflection is done in procedures like endoscopy and laser surgery. These procedures make the light transmit in a desirable manner to pass inside the human body.

Endoscopy

A thin, flexible tube containing fiber optic cables is inserted into the body.
Light travels through the fibers using TIR. This allows doctors to see the image of internal organs like the stomach, colon, or lungs.

Laser Surgery

Laser beams are delivered via fiber optics to perform major surgeries like the removal of tumors or retina, cornea problems..
TIR is done to pass the laser light without any.

These methods provide more precise, simpler, quicker and safer solutions for diagnosis and therapy. Even though the internal structures are complex, TIR makes light focused on its way.

Measuring Refractive Index Using the Critical Angle Method

A simple and precise approach for determining a substance’s refractive index is the critical angle method. Here is how it determines the refractive index.

A light ray is directed from the sample which is in denser medium as compared to air being a rarer medium.
The angle of incidence is increased until the refracted ray just disappears, and the ray travels along the boundary. Now, the critical angle is created.

Using the formula:

μ=1/sinθc

we can find the refractive index of the sample. This technique is often used in:

Chemistry labs for purity testing.
Food and beverage industry to determine sugar content.
Quality control of transparent materials like glass and plastics.

Thus, TIR is not just a theoretical concept, but a mathematical tool to make precise measurements

Common Misconceptions About Total Internal Reflection

TIR may be confusing sometimes. Major misconceptions about it are as follows:

TIR can happen when light goes from air to water.
TIR only occurs only when light wanders from a denser to a rarer medium.
TIR is a process of reflection.
Not almost true. It undergoes strong refraction before reflection.
Any angle can create TIR.
TIR strongly demands for the angle of incidence greater than the critical angle.
Mirrors and TIR work the same way.
Mirrors reflect light using a metallic coating, while TIR is a natural internal process with no loss in light transmission.

These misconceptions must be cut-out to understand TIR, critical angle and refraction properly.

Simple Classroom Experiments Demonstrating TIR

TIR can be demonstrated easily in a classroom.

Water and light Experiment:

Use a laser light in a transparent tank filled with water.
Point the light beam and keep increasing the angle.
Finally the beam reflects from inside the tank. This is the TIR.

Fiber Optic experiment:

Use a plastic rod or actual fiber optic cable.
Serve light into one end of a cable and see it coming out from the other end. What you observe is the TIR of light.

These experiments not only illustrate the concept of TIR but also give a clear view of the practical implication of TIR. They are safe, highly visual and easily attainable which makes them perfect for high school education.

Conclusion

Total Internal Reflection is a leading phenomena in optics. Its simpler but powerful results is the reason we are surrounded by technologies made from TIR. Not only a technology, it is a beautiful natural phenomena that explains the beauty of gems and stars. Thus, it is the most versatile phenomena of physics. To obtain it, one must take care of the medium light travels through and the angle of incidence it makes.

All our health status, communication status and vision standards are influenced by Total Internal Reflection. It is not that complex if proper attention is given to its requirements. Thus, it can be easily demonstrated within a classroom, without the need of costly apparatus. To sum up, knowingly or unknowingly, we have always been surrounded by TIR.

References

Learning, L. (2021). Total Internal Reflection. Fundamentals of Heat, Light & Sound.

Harrick, N. J. (1963). Total internal reflection and its application to surface studies. Annals of the New York Academy of Sciences, 101(3), 928-959.

Uranus, H. P. (2005). Guiding light by and beyond the total internal reflection mechanism.

Kneebone, R. (2002). Total internal reflection: an essay on paradigms. Medical education, 36(6), 514-518.

Mahan, A. I., & Bitterli, C. V. (1978). Total internal reflection: a deeper look. Applied Optics, 17(4), 509-519.