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# Total Internal Reflection     ## Introduction to Total Internal Reflection

Last updated date: 29th Jan 2023
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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.

### 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

1. 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.

1. 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.

1. 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

1. 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.

1. 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. If an optical fibre is having a refractive index of n1 = 2 enclosed by another glass of refractive index n2. Calculate the value of other glass’s refractive index such that the critical angle between the two cladding is 60°.

Data given,

• Critical angle, θ = 60°

• Refractive index, n1 = 2

• Refractive index n2 =?

To calculate n2, the formula is Sin θ = n2/n1

Sin 60°= n2 / 2

or, n2 =2 × sin 60°

or, n2= 1.732

2. What is the value of the refractive index of a glass which has the critical angle of 45°?

Data given,

• Critical angle θ = 45°

• Refractive index of the medium, μ = ?

According to formula,

μ = 1 / sin θ

μ = 1 / sin 450

μ= 1 / 0.5

µ = 2

3. Define refractive index in simple terms.

Refractive index is the measurement of the curving of a ray that passes from one medium to another medium.

We can find the value of the refractive index with the formula, n = c / v

4. What is the reason behind the reflection of light?

Reflection of light is also another form of electromagnetic radiation. This happens when the incident rays face a surface or a boundary that consumes the energy of the radiation and returns the waves away from the incidence surface.

5. What are some real-life examples for total internal reflection?

Two of the very common example which we can see in our daily lives confirming total internal reflection are:

Diamond:

The incident ray falls on every facet of the diamond, forming an angle greater than the critical angle. The diamond's critical value is 23°. This situation is responsible for a diamond's total internal reflection, which causes it to shine.

Mirage:

The water layer appears at short distances in the desert or on the road due to an optical illusion. Hence, a mirage is an example of total internal reflection, which occurs as a result of atmospheric refraction.

6. What are the conditions required and certain consequences for the total internal reflection?

Following are the conditions required:

• The angle of incidence in the denser medium must be greater than the critical angle for that pair of media for the effect to be observed.

• To be effective, a ray of light must travel from a denser to a rarer medium.

Following are the Consequences:

• A crack in a glass vessel frequently reflects light in the same way as a mirror would do.

• The light reflects off of a diamond when it is viewed from particular angles.

• If you look at it from certain angles, an empty test tube with water in a beaker glows like a mirror.

7. How are Reflection and Refraction distinguished?

Reflection is the phenomenon of light reflecting back when it hits a smooth surface.

Nature of Surface: Occurs on shiny surfaces.

Types: Two forms: Regular and Diffuse reflection.

Occurrence: Mirror occurrence.

The behavior of Light: Light bounces and returns in the same direction.

Speed of Light: Does not vary.

Medium of Light Propagation: Remains the same.

The angle of Reflection And Angle of Incidence: It is the same.

Light beams bend as they pass from one medium to another, and this is known as refraction.

Nature of Surface: This occurs in transparent surfaces that allow bending of the ray to a different medium.

Types: Single form of refraction.

Occurrence: Occurs in lenses.

Behavior of Light: Light changes path.

Speed of Light: Varies with the medium.

Medium of Light Propagation: Gets changed.

The Angle of Reflection and Incidence: It is not the same.

8. Is it true that rainbows develop as a result of total interior reflection?

Yes. Rainbows are only visible when light rays are reflected inside raindrops. The shape of raindrops is spherical.

When sunlight strikes airborne drops, it is refracted. Sunlight consists of a spectrum of colors, each with its unique wavelength.

As a result, each color refracts at a unique angle. All of these colors are reflected inside the drop if the angle is greater than the critical angle.

The colors are refracted even more as they leave the drop. As a result, we observe different rainbow colors.

9. Define Refractive Index?

The bending of a beam of light as it passes through one medium and into another is measured by the refractive index, also known as the index of refraction.

Let’s take

I = The angle of incidence of a ray in a vacuum

R = The angle of refraction

Therefore, the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction; n = sin I / sin r.

Students can get detailed information about Total Internal Reflection at Vedantu’s website.

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