What is Total Internal Reflection? Discover how light behaves between different media and the science behind total internal reflection (TIR).

Introduction

TIR is one of the most remarkable phenomena in optics. It explains many interesting optical effects observed in nature and technology, including the formation of mirages on hot roads.

However, to understand TIR, we first need to understand how light behaves when it travels between different media.

What is Total Internal Reflection? _ Illustration of The Behaviour of Light between Different Media

When light passes from one medium to another—such as from air to water or glass—its speed changes. This change in speed causes the light ray to bend at the boundary between the two materials.

The bending of light is known as refraction, and it depends on the optical density and refractive index of the media involved.

Let us try to understand how light behaves when it travels from one material to another.

Refraction of Light

Refraction is the bending of light as it passes from one medium into another with a different optical density. This occurs because light travels at different speeds in different materials.

Optical Density

It is the property of a medium that determines how much it reduces the speed of light passing through it.

A medium in which light travels more slowly is said to be optically denser, while a medium in which light travels faster is optically rarer.
In optics, it is related to the refractive index of the medium.

Thus, it is inversely proportional to the speed of light in the medium:

$\text{Optical Density} \propto \dfrac{1}{\text{Speed of Light in the Medium}}$

Direction of Bending

The direction in which light bends depends on the optical densities of the two media:

Situation	Direction of Bending
Rarer → Denser (air → glass)	Light bends toward the normal
Denser → Rarer (glass → air)	Light bends away from the normal

The normal is an imaginary line drawn perpendicular to the surface at the point where the light ray strikes.

Example

For example:

Light travels fastest in a vacuum
Slightly slower in the air
Slower still in water
Even slower in glass

When light enters a material where it travels more slowly, its direction changes.

Refractive Index

The extent to which light bends when entering a medium depends on the refractive index of that material.

The refractive index $n$ is defined as:

$n = \dfrac{\text{Speed of light in vacuum}}{\text{Speed of light in the medium}}$

Typical values of $n$ include:

Medium	Refractive Index
Air	~1.0003
Water	~1.33
Glass	~1.5

A higher refractive index means light travels more slowly in that material.

Total Internal Reflection

TIR is one of the most important phenomena in optics. It occurs when light attempts to move from a denser medium into a rarer medium.

Increasing the Angle of Incidence

Imagine a beam of light travelling from glass into air.

What is Total Internal Reflection? _ Illustration of Bending of Light

As the angle of incidence (the angle between the incident ray and the normal) increases i.e., $i'' > i' > i$ :

The refracted ray bends away from the normal.
The angle of refraction becomes larger $C > r$ .
Eventually, the refracted ray reaches a maximum possible value ( $C$ ), called the critical angle.

At this point, something special happens.

The Critical Angle

It is a specific angle of incidence at which the refracted ray travels exactly along the boundary between the two media.

It is represented by $C$ and can be defined as:

“The angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes $90^\circ$ ”.

This means the refracted ray moves along the surface instead of entering the second medium.

Mathematical Relationship

Using Snell’s Law:

$n_1 \sin i = n_2 \sin r$

Where:

$n_1 = \text{refractive index of the denser medium}$
$n_2 = \text{refractive index of the rarer medium}$
$i = \text{angle of incidence}$
$r = \text{angle of refraction}$

At the critical angle:

$i = C, \qquad r = 90^\circ$

Substituting into Snell’s Law:

$n_1 \sin C = n_2 \sin 90^\circ$

Since;

$\sin 90^\circ = 1$

Hence;

$n_1 \sin C = n_2$

$\sin C = \dfrac{n_2}{n_1}$

If the rarer medium is air, then

$n_2 \approx 1$

Therefore;

$\sin C = \dfrac{1}{n}$

Here, $n = n_1$ is the refractive index of the denser medium.

Hence, the angle $C$ is:

$C = \sin^{-1}\!\left(\dfrac{1}{n}\right)$

For glass, the critical angle is approximately $45^\circ$ .

What is Total Internal Reflection?

TIR can be defined as:

“The phenomenon in which a light ray traveling from a denser medium to a rarer medium is completely reflected into the denser medium when the angle of incidence becomes greater than the critical angle, so that no refraction occurs in the rarer medium”.

“The complete reflection of light back into a denser medium when it travels toward a rarer medium, and the angle of incidence exceeds the critical angle”.

Unlike ordinary reflection from mirrors, TIR has almost no loss of light intensity.

Conditions for Total Internal Reflection

Two conditions must be satisfied for TIR to occur:

1. Light must travel from a denser medium to a rarer medium

Examples include:

Glass (denser) → Air (rarer)
Water (denser) → Air (rarer)

If light travels from air to glass, total internal reflection cannot occur.

2. The angle of incidence must exceed the critical angle

If the angle is smaller than the critical angle, light will simply refract.

Mirage | A Natural Optical Illusion

Mirage is one of the fascinating phenomena related to TIR. They are commonly observed on hot roads or deserts, where the ground appears to be covered with water.

Temperature Layers in Air

On a hot day, air near the ground becomes very hot and less dense, while the air above remains cooler and denser.

This creates multiple layers of air with gradually changing refractive indices.

How does a Mirage Form?

Light from the sky travels downward through these layers.

As it passes through the changing air density:

The light ray bends gradually.
Eventually, it reaches an angle greater than the critical angle.
Total internal reflection occurs.

The reflected ray reaches the observer’s eye.

Why the Road Looks Wet

Because the light originates from the sky but reaches the eye from the ground, the brain interprets it as a reflection from water.

This produces the illusion of a shiny water surface on the road.

Rainbows | Optical Masterpiece of Nature

One of the most beautiful natural displays of light is the rainbow. It is a multicoloured arc seen in the sky after rainfall.

What is Rainbow? _ Illustration of Optical Masterpiece of Nature

To observe a rainbow:

The Sun must be behind the observer
Rain must be in front

A rainbow is essentially a natural solar spectrum.

How does a Rainbow Form?

After rain, millions of tiny raindrops remain suspended in the air.
Each raindrop acts like a tiny prism.
Inside each drop, sunlight undergoes:
- Refraction when entering the drop
- Total internal reflection inside the drop
- Refraction again when leaving the drop

During this process, light is dispersed into different colours.

Difference between Primary Rainbow and Secondary Rainbow

Feature	Primary Rainbow	Secondary Rainbow
Definition	The most common and brightest rainbow is seen after rainfall.	A second, fainter rainbow that sometimes appears outside the primary rainbow.
Optical Process	Light undergoes two refractions and one total internal reflection inside the raindrop.	Light undergoes two refractions and two total internal reflections inside the raindrop.
Brightness	Brighter and more clearly visible.	Fainter and less bright compared to the primary rainbow.
Position in the Sky	Appears closer to the centre of the rainbow arc.	Appears outside and above the primary rainbow.
Colour Arrangement	Red is on the outer edge and violet on the inner edge.	Violet is on the outer edge and red on the inner edge (reversed order).
Colour Order	Red → Orange → Yellow → Green → Blue → Indigo → Violet	Violet → Indigo → Blue → Green → Yellow → Orange → Red

Difference between Primary Rainbow vs Secondary Rainbow

Conclusion

The study of light reveals an extraordinary world of optical phenomena, and TIR is one such fascinating optical phenomenon. It plays a key role in both nature and technology.

By understanding how light behaves between different media—bending, slowing down, or speeding up—we can explain why TIR occurs and why phenomena like mirages appear on hot roads or in deserts.

TIR is the foundation of many modern applications, including:

Optical instruments
Fibre-optic communication
Medical imaging technologies

Frequently Asked Questions (FAQs)

What is total internal reflection (TIR)?

TIR is the complete reflection of light back into a denser medium when the angle of incidence exceeds the critical angle at the boundary with a rarer medium.

How does total internal reflection occur?

TIR occurs when light travels from a medium with a higher refractive index to one with a lower refractive index, and the angle of incidence is greater than the critical angle.

What is the critical angle in optics?

It is the specific angle of incidence in the denser medium at which the refracted light travels along the boundary (angle of refraction = 90°).

What is the difference between refraction and total internal reflection?

Refraction is the bending of light as it passes into another medium, while TIR is when light does not enter the second medium and is fully reflected.

Why does total internal reflection only occur from denser to rarer media?

Only when light goes from a higher refractive index to a lower one can the refracted ray reach an angle of 90°, enabling TIR.

What are real-life examples of total internal reflection?

Examples include mirages on hot roads, optical fibres, diamonds’ sparkle, and endoscopes in medical imaging.

How is the refractive index related to total internal reflection?

The refractive index determines how much light bends in a medium, and it is used to calculate the critical angle required for TIR to occur.

Can total internal reflection occur in water?

Yes. Light moving from water (denser) to air (rarer) can undergo TIR if the angle of incidence is greater than the water‑air critical angle.

What is a mirage, and how is it formed?

A mirage is an optical illusion caused by TIR in layers of air with different temperatures, making the ground appear reflective like water.

What are the applications of total internal reflection in technology?

TIR is used in fibre‑optic cables, binoculars, prisms, optical sensors, and medical imaging devices because it allows light to travel long distances with minimal loss.

What is Total Internal Reflection? | 101 Guide | Simplified

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